frontiers / frontier
Erdős problems frontier
- id
- vfr_37aec80d874a0239
- license
- CC-BY-4.0
- findings
- 1,256
- accepted core
- 6
- contested
- 0
- links
- 17
- sources
- 1,234
- evidence
- 1,256
- avg conf
- 0.98
e1271/1271 · statement.attested · reviewer:will-blair · 2026-06-10 · null→null
Findings dataset
machine packet · packet.jsonsha256:8d3b79666519c4dd…1256 rows, every one a fold over the signed log. Scrub the event ruler and the table reduces to that prefix.
type1256/1256 rows
| id | claim | grade | conf | verifier | witness | last event |
|---|---|---|---|---|---|---|
| vf_0048a13ac8707d73 | Erdős Problem #105 has status 'disproved (lean)'. Topics: geometry. Erdős prize: $50. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_0085928f0ac67d01 | Erdős Problem #40 remains OPEN. Statement: For what functions $g(N) → \infty$ is it true that $$\lvert A\cap \{1,\ldots,N\}\rvert \gg \frac{N^{1/2}}{g(N)}$$ implies $\limsup 1_A\ast 1_A(n)=\infty$? Topics: number theory, additive basis. Erdős prize: $500. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_00cdc486fa764069 | Erdős Problem #461 remains OPEN. Topics: number theory, primes. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_00dc0ceaaa58ab77 | Erdős Problem #861 is SOLVED. Topics: number theory, sidon sets. Erdős prize: no. Not yet formalized in Lean. OEIS: A143824, A227590, A003022, A143823. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_00e14bb157245345 | Erdős Problem #71 has been PROVED (Erdős's conjecture holds). Topics: graph theory, cycles. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_0106baf19a411342 | Erdős Problem #641 has been DISPROVED (a counterexample is known). Topics: graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_01262901c2f60e1f | Erdős Problem #343 has been PROVED (Erdős's conjecture holds). Topics: number theory, complete sequences. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_0139666d12dffaf1 | Erdős Problem #903 has been PROVED (Erdős's conjecture holds). Topics: combinatorics. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_01468af98db2dcec | Erdős Problem #610 has been PROVED (Erdős's conjecture holds). Topics: graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_017fe040a7805919 | Erdős Problem #749 remains OPEN. Statement: Let $\epsilon>0$. Does there exist $A\subseteq \mathbb{N}$ such that the lower density of $A+A$ is at least $1-\epsilon$ and yet $1_A\ast 1_A(n) \ll_\epsilon 1$ for all $n$? Topics: additive combinatorics. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_0188a388ddc15094 | Erdős Problem #802 remains OPEN. Topics: graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_0196f7cbc35ff04c | Erdős Problem #186 is SOLVED. Topics: additive combinatorics. Erdős prize: no. Not yet formalized in Lean. OEIS: A389784. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_019dee951cce3bf1 | Erdős Problem #719 remains OPEN. Topics: graph theory, hypergraphs. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_021aab0b6de8d3cb | Erdős Problem #14 remains OPEN. Topics: number theory, sidon sets, additive combinatorics. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A143824, possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_026b6ca358fed4f3 | Erdős Problem #795 has been PROVED (Erdős's conjecture holds). Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_02868ab3cae92a4c | Erdős Problem #1002 remains OPEN. Statement: For any $0<\alpha<1$, let $f(\alpha,n)=\frac{1}{\log n}\sum_{1\leq k\leq n}(\tfrac{1}{2}- \{ \alpha k\})$. Does $f(\alpha,n)$ have an asymptotic distribution function? In other words, is there a non-decreasing function $g$ such that $g(-\infty)=0$, $g(\infty)=1$, and $\lim_{n\to \infty}\lvert \{ \alpha\in (0,1): f(\alpha,n)\leq c\}\rvert=g(c)$? Topics: analysis, diophantine approximation. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_02969d7f9dcc0e53 | Erdos-Turan additive-bases conjecture (1941, open): for every additive basis A of order h for the natural numbers, the representation function r_A(n) cannot be bounded. The h=2 case is open. | unreviewed | 0.70 | — | — | asserted · 13d |
| vf_03626bce7a8762ec | Erdős Problem #224 has status 'proved (lean)'. Topics: geometry. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_0373423a49fad2cf | Erdős Problem #1044 has status 'solved (lean)'. Topics: analysis. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_03a9fba560346442 | Erdős Problem #440 is SOLVED. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_03c1319b9c297377 | Erdős Problem #1094 remains OPEN. Statement: For all $n\ge 2k$ the least prime factor of $\binom{n}{k}$ is $\le\max(n/k,k)$, with only finitely many exceptions. Topics: number theory, binomial coefficients. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | noted · 2d |
| vf_040c9e1af984d1cd | Erdős Problem #360 is SOLVED. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_0470b20ce0614e6a | Erdős Problem #297 is SOLVED. Topics: number theory, unit fractions. Erdős prize: no. Not yet formalized in Lean. OEIS: A092670. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_04c2ff267458866e | Erdős Problem #30 remains OPEN. Statement: Is it true that, for every $\varepsilon > 0$, $h(N) = \sqrt N + O_{\varespilon}(N^\varespilon) Topics: number theory, sidon sets, additive combinatorics. Erdős prize: $1000. Statement is machine-verified in Lean (formal-conjectures). OEIS: A143824, A227590, A003022. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_04c492c383a7fe0f | Erdős Problem #858 is SOLVED. Topics: number theory, primitive sets. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_04e4c16556885139 | Erdős Problem #116 has been PROVED (Erdős's conjecture holds). Topics: polynomials, analysis. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_053e25a6ea259bf2 | Erdős Problem #898 has status 'proved (lean)'. Topics: geometry. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_05646653e3dfc403 | Erdős Problem #539 remains OPEN. Statement: Let $h(n)$ be maximal such that, for any set $A\subseteq \mathbb{N}$ of size $n$, the set$$\left\{ \frac{a}{(a,b)}: a,b\in A\right\}$$has size at least $h(n)$. Estimate $h(n)$. Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_05d605b86a00e60a | Erdős Problem #517 remains OPEN. Statement: If `f(z) = ∑ aₖzⁿₖ` is an entire function (with `aₖ ≠ 0` for all `k`) such that `nₖ / k → ∞`, is it true that `f` assumes every value infinitely often? Topics: analysis. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_0603f7eaae023345 | Erdős Problem #382 remains OPEN. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: A388850. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_063bab00e027b681 | Erdős Problem #176 remains OPEN. Topics: additive combinatorics, arithmetic progressions, discrepancy. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_064b77c798d85c77 | Erdős Problem #1126 has status 'proved (lean)'. Topics: analysis. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_0666e94eb74c8d1f | Erdős Problem #321 remains OPEN. Statement: Let $R(N)$ be the size of the largest $A\subseteq\{1, ..., N\}$ such that all sums $\sum_{n\in S} \frac{1}{n}$ are distinct for $S\subseteq A$. What is $R(N)$? Topics: number theory, unit fractions. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A384927, A391592. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_06be95639f23308d | Erdős Problem #867 has status 'disproved (lean)'. Topics: additive combinatorics. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_06d37e001d97c12a | Erdős Problem #1110 remains OPEN. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_07016e0ae3322782 | Erdős Problem #1079 is SOLVED. Topics: graph theory, turan number. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_073a4860f559691c | Erdős Problem #551 has status 'decidable'. Topics: graph theory, ramsey theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_0771bc2fb1845406 | Erdős Problem #129 remains OPEN. Topics: graph theory, ramsey theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_0776be3418b5f4fe | Erdős Problem #391 has been PROVED (Erdős's conjecture holds). Topics: number theory, factorials. Erdős prize: no. Not yet formalized in Lean. OEIS: A034258, A034259. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_07d733d5a80132f7 | Erdős Problem #642 remains OPEN. Topics: graph theory, cycles. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_08178413a9f2bbc8 | Erdős Problem #666 has status 'disproved (lean)'. Topics: graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_08b5a08c46a0586e | Erdős Problem #136 is SOLVED. Topics: graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_08bd57c59b12785a | Erdős Problem #952 remains OPEN. Statement: Is there an infinite sequence of distinct Gaussian primes $x_1,x_2,\ldots$ such that $\lvert x_{n+1}-x_n\rvert \ll 1$? Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_08f314f7490c0daf | Erdős Problem #951 remains OPEN. Statement: If `1 < a 0 < ...` has property `Erdos951Prop`, is it true that `#{a i ≤ x} ≤ π x`? Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_091ca3d36587de42 | Erdős Problem #456 remains OPEN. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_094c9c24076da25b | Erdős Problem #914 has status 'proved (lean)'. Topics: graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_098e97569a5632f4 | Erdős Problem #748 has been PROVED (Erdős's conjecture holds). Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: A007865. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_09b1a48e9ae0cb38 | Erdős Problem #623 remains OPEN. Statement: Let $X$ be a set of cardinality $\aleph_\omega$ and $f$ be a function from the finite subsets of $X$ to $X$ such that $f(A)\not\in A$ for all $A$. Must there exist an infinite $Y\subseteq X$ that is independent - that is, for all finite $B\subset Y$ we have $f(B)\not\in Y$? Topics: set theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_0a0d6c8f246a7f51 | Erdős Problem #53 has been PROVED (Erdős's conjecture holds). Topics: number theory, additive combinatorics. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_0a6b597f1010c0f1 | Erdős Problem #603 remains OPEN. Topics: combinatorics, set theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_0a93b01d28c3488e | Erdős Problem #73 has been PROVED (Erdős's conjecture holds). Topics: graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_0ac1e93bfc506dac | Erdős Problem #933 remains OPEN. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_0ac9a7bb80e369a2 | Erdős Problem #530 remains OPEN. Topics: number theory, sidon sets. Erdős prize: no. Not yet formalized in Lean. OEIS: A143824, possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_0ba39f905a01ec35 | Erdős Problem #49 has been PROVED (Erdős's conjecture holds). Topics: number theory, primes. Erdős prize: no. Not yet formalized in Lean. OEIS: A365339, A365474. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_0ba7136590fcf28f | Erdős Problem #353 has been PROVED (Erdős's conjecture holds). Topics: geometry. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_0bdc86f4d9f9ea18 | OBLIGATION (Erdos #124). BANKED: the reservoir criterion verified on the BEGL case {3,4,7}, k=1. OPEN: uniform L-syndeticity across all cases remains open. | unreviewed | 0.50 | — | — | asserted · 2d |
| vf_0be66dd29cc9e124 | Erdős Problem #1211 is SOLVED. Topics: number theory, ramsey theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_0c0fe3d87b4e0464 | Erdős Problem #249 remains OPEN. Statement: Is $$\sum_{n} \frac{\phi(n)}{2^n}$$ irrational? Here $\phi$ is the Euler totient function. Topics: number theory, irrationality. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A256936. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_0c4199641e16bfae | Erdős Problem #157 has been PROVED (Erdős's conjecture holds). Topics: sidon sets. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_0c84ea2c0b448ec1 | Erdős Problem #1048 has status 'disproved (lean)'. Topics: analysis. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_0cb778342859402c | Erdős Problem #1043 has status 'disproved (lean)'. Statement: **Erdős Problem 1043**: Let $f\in \mathbb{C}[x]$ be a monic polynomial. Must there exist a straight line $\ell$ such that the projection of $$\{ z: \lvert f(z)\rvert\leq 1\}$$ onto $\ell$ has measure at most $2$? Pommerenke [Po61] proved that the answer is no. This was formalized in Lean by Alexeev using Aristotle. Topics: analysis. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_0cf052d918abf92d | Erdős Problem #219 has been PROVED (Erdős's conjecture holds). Statement: Are there arbitrarily long arithmetic progressions of primes? Solution: yes. Ref: Green, Ben and Tao, Terence, _The primes contain arbitrarily long arithmetic progressions_ Topics: number theory, additive combinatorics, primes, arithmetic progressions. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A005115, A113827, A123556. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_0cfd7473cd877296 | Erdős Problem #544 remains OPEN. Topics: graph theory, ramsey theory. Erdős prize: no. Not yet formalized in Lean. OEIS: A000791. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_0d26c6346393db4e | Erdős Problem #972 remains OPEN. Statement: **Erdős problem 972.** Let $\alpha > 1$ be irrational. Are there infinitely many primes $p$ such that $\lfloor p\alpha \rfloor$ is also prime? Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_0d4ac181db98ceaa | OBLIGATION (Erdos #203). BANKED: a partial CRT covering certificate (m + 20 prime rows, ~0.7467 density) verified (crt_partial_cover). OPEN: extend to a full cover (the verified rows do not cover all residues). | unreviewed | 0.50 | — | — | asserted · 2d |
| vf_0d9d999ab61f61f0 | Erdős Problem #150 has status 'proved (lean)'. Topics: graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_0dc5e31b8bd41bba | Erdős Problem #875 remains OPEN. Topics: additive combinatorics. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_0df74608a9e1d617 | Erdős Problem #324 remains OPEN. Statement: Does there exist a polynomial $f(x)\in\mathbb{Z}[x]$ such that all the sums $f(a)+f(b)$ with $a < b$ nonnegative integers are distinct? Topics: number theory, powers. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_0e3bda3eef189447 | Erdős Problem #45 has status 'proved (lean)'. Topics: number theory, unit fractions, ramsey theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_0e4d9ed4cd5ba437 | Erdős Problem #252 remains OPEN. Statement: Erdős Problem 252: irrationality of the sum for a given $k$. Topics: number theory, irrationality. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A227988, A227989, possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_0e75cda6c19edbd5 | Erdős Problem #948 remains OPEN. Topics: number theory, ramsey theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_0e89db391781fe60 | Erdős Problem #659 has status 'proved (lean)'. Statement: Is there a set of $n$ points in $\mathbb{R}^2$ such that every subset of $4$ points determines at least $3$ distances, yet the total number of distinct distances is $\ll \frac{n}{\sqrt{\log n}}$? There does exist such a set: a suitable truncation of the lattice $\{(a,b\sqrt{2}): a,b\in\mathbb{Z}\}$ suffices. This construction appears to have been first considered by Moree and Osburn \cite{MoOs06}, who proved that it has $\ll \frac{n}{\sqrt{\log n}}$ many distinct distances. This construction was independently found by [Lund and Sheffer](https://adamsheffer.wordpress.com/2014/07/16/point-sets-with-few-distinct-distances/), who further noted that this configuration contains no squares or equilateral triangles. There are only six possible configurations of $4$ points which determine only $2$ distances (first noted by Erdős and Fishburn [ErFi96]), and five of them contain either a square or an equilateral triangle. The remaining configuration contains four points from a regular pentagon, and Grayzel [Gr26] (using Gemini) has noted in the comments that this configuration can also be ruled out, thus giving a complete solution to this problem. Boris Alexeev provides a formalisation of the reduction, which is conditional on Bernays' theorem (assumed as an axiom in the proof to obtain the $O(n/\sqrt{\log n})$ bound). See the [formal proof](https://github.com/plby/lean-proofs/blob/226d5fad7143dcebea2bbb5ec87f18a3a1dcea69/src/v4.24.0/ErdosProblems/Erdos659.lean). Topics: geometry, distances. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_0ead73839ac27764 | Erdős Problem #1209 remains OPEN. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_0f1a2b3f426b98cf | Erdős Problem #682 has been PROVED (Erdős's conjecture holds). Topics: number theory, primes. Erdős prize: no. Not yet formalized in Lean. OEIS: A386978. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_0f29bb6c261c14ec | Erdős Problem #1 remains OPEN. Statement: If $A\subseteq\{1, ..., N\}$ with $|A| = n$ is such that the subset sums $\sum_{a\in S}a$ are distinct for all $S\subseteq A$ then $$ N \gg 2 ^ n. $$ Topics: number theory, additive combinatorics. Erdős prize: $500. Statement is machine-verified in Lean (formal-conjectures). OEIS: A276661. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_0f8665c0d610d60b | Erdős Problem #117 remains OPEN. Topics: group theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_0f9e4ec8e2247c97 | Erdős Problem #86 remains OPEN. Topics: graph theory. Erdős prize: $100. Not yet formalized in Lean. OEIS: A245762. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_107b1871b42eefcd | Erdős Problem #298 has status 'proved (lean)'. Statement: Does every set $A \subseteq \mathbb{N}$ of positive density contain some finite $S \subset A$ such that $\sum_{n \in S} \frac{1}{n} = 1$? The answer is yes, proved by Bloom [Bl21]. This was formalized in Lean 3 by Bloom and Mehta. Topics: number theory, unit fractions. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_109a6f252ea91c50 | Erdős Problem #606 is SOLVED. Topics: geometry. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_10a63b0491d11843 | Erdős Problem #70 remains OPEN. Topics: graph theory, ramsey theory, set theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_10c07a15cb407069 | Erdős Problem #1076 has been PROVED (Erdős's conjecture holds). Topics: hypergraphs. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_10ccaee041fcafe1 | Erdős Problem #773 remains OPEN. Topics: number theory, sidon sets, squares. Erdős prize: no. Not yet formalized in Lean. OEIS: A390813. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_10f96bbffa8af50b | Erdős Problem #68 remains OPEN. Statement: Is $$\sum_{n=2}^\infty \frac{1}{n!-1}$$ irrational? Topics: number theory, irrationality. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A331373. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_113dea72070e740c | Erdős Problem #331 has status 'disproved (lean)'. Statement: Let $A,B\subseteq \mathbb{N}$ such that for all large $N$$$\lvert A\cap \{1,\ldots,N\}\rvert \gg N^{1/2}$$and$$\lvert B\cap \{1,\ldots,N\}\rvert \gg N^{1/2}.$$ Is it true that there are infinitely many solutions to $a_1-a_2=b_1-b_2\neq 0$ with $a_1,a_2\in A$ and $b_1,b_2\in B$? Ruzsa has observed that there is a simple counterexample: take $A$ to be the set of numbers whose binary representation has only non-zero digits in even places, and $B$ similarly but with non-zero digits only in odd places. It is easy to see $A$ and $B$ both grow like $\gg N^{1/2}$ and yet for any $n\geq 1$ there is exactly one solution to $n=a+b$ with $a\in A$ and $b\in B$. This was formalized in Lean by van Doorn using Aristotle. Topics: number theory, additive combinatorics. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_1158951b1d1f3ceb | Erdős Problem #804 has been DISPROVED (a counterexample is known). Topics: graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_117e3ea46e0a5e1f | Erdős Problem #1148 has status 'proved (lean)'. Statement: Can every large integer $n$ be written as $n=x^2+y^2-z^2$ with $\max(x^2,y^2,z^2)\leq n$? This was proved affirmatively by Chojecki [Ch26], using a Duke-type equidistribution theorem. A Lean formalisation of the reduction (conditional on a Duke-type equidistribution theorem) exists; see the [forum discussion](https://www.erdosproblems.com/forum/thread/1148#post-4849). Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A390380, A393168. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_11876b60a4e6d6a7 | Erdős Problem #616 remains OPEN. Topics: graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_11af2f3b64fb0385 | Erdős Problem #472 remains OPEN. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: A389713, possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_125d481fdd040806 | Erdős Problem #158 remains OPEN. Statement: Let `A` be an infinite `B₂[2]` set. Must `liminf |A ∩ {1, ..., N}| * N ^ (- 1 / 2) = 0`? Topics: sidon sets. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_1270769ad30226d8 | Erdős Problem #679 remains OPEN. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_1299f5a17e01265d | Erdős Problem #992 has been DISPROVED (a counterexample is known). Topics: discrepancy. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_12b985c463f74664 | Erdős Problem #990 has status 'disproved (lean)'. Topics: analysis. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_12b9e31e7f1a0dbd | Erdős Problem #92 has been DISPROVED (a counterexample is known). Topics: geometry, distances. Erdős prize: $500. Statement is machine-verified in Lean (formal-conjectures). OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_12edf5d520c20c45 | Erdős Problem #295 remains OPEN. Statement: Let $k(N)$ denote the smallest $k$ such that there exists $N ≤ n_1 < ⋯ < n_k$ with $\frac 1 {n_1} + ... + \frac 1 {n_k} = 1$ Is it true that $\lim_{N \to \infty} k(N) - (e - 1)N = \infty$? Topics: number theory, unit fractions. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A192881. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_12fd8cce1b371d03 | Erdős Problem #328 has been DISPROVED (a counterexample is known). Topics: number theory, additive combinatorics. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_1321ba201d47f508 | Erdős Problem #64 has status 'falsifiable'. Statement: Does every finite graph with minimum degree at least $3$ contain a cycle of length $2^k$ for some $k \geq 2$? Topics: graph theory, cycles. Erdős prize: $1000. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_1336b24b8e3c7b0d | Erdős Problem #1019 has been PROVED (Erdős's conjecture holds). Topics: graph theory, planar graphs. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_141070e9d1a680d0 | Erdős Problem #732 has been PROVED (Erdős's conjecture holds). Topics: combinatorics. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_14235812215845bc | Erdős Problem #270 has been DISPROVED (a counterexample is known). Topics: irrationality. Erdős prize: no. Not yet formalized in Lean. OEIS: A073016. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_1443e92491539657 | Erdős Problem #499 has status 'proved (lean)'. Topics: combinatorics. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_147886465f122cc4 | Erdős Problem #829 remains OPEN. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_14bba1f603a0e205 | Erdős Problem #643 remains OPEN. Topics: graph theory, hypergraphs. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_14dc2a46431d6d48 | Erdős Problem #811 remains OPEN. Topics: graph theory, ramsey theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_15066d0a0ab73d8f | Erdős Problem #764 has been DISPROVED (a counterexample is known). Topics: number theory, additive combinatorics. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_152b59acf52f9874 | Erdős Problem #498 has status 'proved (lean)'. Topics: combinatorics, analysis. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_15940eef97d062ea | Erdős Problem #602 remains OPEN. Statement: Does every almost-disjoint family of countably infinite sets whose pairwise intersections all have size ≠ 1 have Property B? Formally: let `α` be any type, let `(A_i)_{i ∈ I}` be a family of countably infinite subsets of `α` such that for all `i ≠ j`, the intersection `A_i ∩ A_j` is finite and `|A_i ∩ A_j| ≠ 1`. Does there exist a 2-colouring `f : α → Fin 2` such that no `A_i` is monochromatic? This is an open question about Property B for almost-disjoint families with a forbidden intersection size of 1. **Note:** This generalises the formulation in which the ground set is `ℕ`. Since every countably infinite set is in bijection with `ℕ`, the two formulations are equivalent, but working over an arbitrary ground type makes the statement apply immediately to, e.g., almost-disjoint families of countable subsets of an uncountable space. Topics: combinatorics, set theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_15bf4bec4cd8134f | Erdős Problem #237 has status 'proved (lean)'. Topics: number theory, primes. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_15db0f359d848eed | Erdős Problem #1191 remains OPEN. Topics: additive combinatorics, sidon sets. Erdős prize: $1000. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_15dc5ce433b11d94 | Erdős Problem #593 remains OPEN. Statement: **Erdős Problem 593 ($500)**: Characterize those finite 3-uniform hypergraphs which appear in every 3-uniform hypergraph of chromatic number $> \aleph_0$. A natural conjectural characterization, recorded here, is that the obligatory finite 3-uniform hypergraphs are exactly the 2-colorable ones (Property B). The forward direction (`IsObligatory → IsTwoColorable`) and converse (`IsTwoColorable → IsObligatory`) are stated as separate variants below; in the graph case ($r = 2$), Erdős–Galvin–Hajnal [EGH75] proved the analogous result (obligatory ⇔ bipartite). Topics: set theory, graph theory, hypergraphs, chromatic number. Erdős prize: $500. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_15e987c69ec8a2d4 | Erdős Problem #364 has status 'verifiable'. Statement: There is no consecutive triple of powerful numbers. Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A060355, A076445. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_15f0719904e3e0a2 | Erdős Problem #720 has been PROVED (Erdős's conjecture holds). Topics: graph theory, ramsey theory. Erdős prize: $100. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_16057fad52e09036 | Erdős Problem #809 remains OPEN. Topics: graph theory, ramsey theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_165f176339d9adca | Erdős Problem #600 remains OPEN. Topics: graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_1673d061620b4644 | Erdős Problem #892 remains OPEN. Topics: number theory, primitive sets. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_16ae5ca22da70669 | Erdős Problem #512 has been PROVED (Erdős's conjecture holds). Topics: analysis. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_16d2ad735d0242f5 | Erdős Problem #1040 remains OPEN. Topics: analysis. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_16db6f3dba299e5f | Erdős Problem #152: machine-found Lean proof published by AlphaProof Nexus (DeepMind, arXiv 2605.22763, May 2026). Independently re-verified locally 2026-06-10: full lake build of google-deepmind/alphaproof-nexus-results@0647711a7118 under their pinned toolchain leanprover/lean4:v4.27.0 succeeded (8062 jobs); static scan clean (no sorry, no native_decide, no custom axioms). Artifacts: erdos_152.lean sha256:fb9cf6bb4de746f9. AI involvement: machine-generated proof, machine-checked (Lean kernel is the referee); statement faithfulness NOT yet independently attested — see paper section 4 for DeepMind's own expert validation. | unreviewed | 0.90 | — | — | attested · 2d |
| vf_171622063c458703 | Erdős Problem #395 has been PROVED (Erdős's conjecture holds). Topics: analysis. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_17356cef05f06e7b | Erdős Problem #106 has status 'falsifiable'. Topics: geometry. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_173f78462d3874e7 | Erdős Problem #668 remains OPEN. Topics: geometry, distances. Erdős prize: no. Not yet formalized in Lean. OEIS: A385657. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_1770045250dffbf6 | Erdős Problem #700 remains OPEN. Topics: number theory, binomial coefficients. Erdős prize: no. Not yet formalized in Lean. OEIS: A091963, possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_17cfee21293efe70 | Erdős Problem #640 remains OPEN. Topics: graph theory, chromatic number. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_17d077ea79b690b8 | Erdős Problem #404 remains OPEN. Topics: number theory, factorials. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_182f281c046c22bf | Erdős Problem #639 has status 'proved (lean)'. Topics: graph theory, ramsey theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_187280ca6f4d09c4 | Erdős Problem #562 remains OPEN. Statement: Let $R_r(n)$ denote the $r$-uniform hypergraph Ramsey number: the minimal $m$ such that if we $2$-colour all edges of the complete $r$-uniform hypergraph on $m$ vertices then there must be some monochromatic copy of the complete $r$-uniform hypergraph on $n$ vertices. Prove that, for $r \ge 3$, $$ \log_{r-1} R_r(n) \asymp_r n, $$ where $\log_{r-1}$ denotes the $(r-1)$-fold iterated logarithm. Topics: graph theory, ramsey theory, hypergraphs. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_18aca0f605965996 | Erdős Problem #55 is SOLVED. Topics: number theory, ramsey theory. Erdős prize: $250. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_18d6b7a5de13859f | Erdős Problem #991 has been PROVED (Erdős's conjecture holds). Topics: discrepancy. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_18e6a86bd3459220 | Erdős Problem #241 remains OPEN. Statement: Is it true that $f(N)\sim N^{1/3}$? Originally asked to Erdős by Bose. This is discussed in problem C11 of Guy's collection [Gu04]. Topics: additive combinatorics, sidon sets. Erdős prize: $100. Statement is machine-verified in Lean (formal-conjectures). OEIS: A387704. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_18ea9179e9c63024 | Erdős Problem #1103 remains OPEN. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: A392164. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_192de23c449c21cb | Erdős Problem #678 has status 'proved (lean)'. Statement: Write $M(n, k)$ be the least common multiple of $\{n+1, \dotsc, n+k\}$. Let $k$ be sufficiently large. Are there infinitely many $m, n$ with $m \geq n + k$ such that $$ M(n, k) > M(m, k + 1) $$? The answer is yes, as proved in a strong form by Cambie [Ca24]. [Ca24] S. Cambie, Resolution of an Erdős' problem on least common multiples. arXiv:2410.09138 (2024). This was formalized in Lean by Alexeev using Aristotle, conditional on asymptotic estimates for the prime counting function (specifically `pi_alt` from the PNT+ project). See the [formal proof](https://github.com/plby/lean-proofs/blob/main/src/v4.24.0/ErdosProblems/Erdos678.lean). Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_195df57eba92c44d | Erdős Problem #133 has been DISPROVED (a counterexample is known). Topics: graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_1a176a6f86851d42 | Erdős Problem #1036 has status 'proved (lean)'. Topics: graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_1a27209c21d11baa | Erdős Problem #357 remains OPEN. Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A364132, A364153, possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_1a316197495c08d0 | Erdős Problem #801 has been PROVED (Erdős's conjecture holds). Topics: graph theory, ramsey theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_1a91ca4eddee0522 | Erdős Problem #683 remains OPEN. Statement: There exists $c > 0$ such that $P(n, k) > \min\{n-k+1, k^{1 + c}\}$ for all $0 < k < n$.} Topics: number theory, primes, binomial coefficients. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A006530, A074399, A121359, possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_1a9c734c4078023e | Erdős Problem #721 is SOLVED. Topics: number theory, additive combinatorics, ramsey theory. Erdős prize: no. Not yet formalized in Lean. OEIS: A171081. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_1ae57f6cde0e3b98 | Erdős Problem #627 remains OPEN. Topics: graph theory, chromatic number. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_1b02c9b209dd10a3 | Erdős Problem #647 has status 'verifiable'. Statement: Let $\tau(n)$ count the number of divisors of $n$. Is there some $n > 24$ such that $$ \max_{m < n}(m + \tau(m)) \leq n + 2? $$ Topics: number theory. Erdős prize: £25. Statement is machine-verified in Lean (formal-conjectures). OEIS: A062249, A087280. | unreviewed | 0.99 | — | — | noted · 2d |
| vf_1b237e9c9612b153 | Erdős Problem #815 has been DISPROVED (a counterexample is known). Topics: graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_1b2f9d0254ab97a3 | Erdős Problem #929 remains OPEN. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_1bf212fa21ded204 | Erdős Problem #970 remains OPEN. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: A048669. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_1c16549cbbeb043d | Erdős Problem #496 has been PROVED (Erdős's conjecture holds). Topics: number theory, diophantine approximation. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_1c75b9b2d853e1bd | Erdős Problem #447 has status 'proved (lean)'. Topics: combinatorics. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_1ceefa8421186fcd | Erdős Problem #628 has status 'falsifiable'. Topics: graph theory, chromatic number. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_1d8e97f73a51640f | Erdős Problem #923 has status 'proved (lean)'. Topics: graph theory, chromatic number. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_1e178c970e204d82 | Erdős Problem #381 has been DISPROVED (a counterexample is known). Topics: number theory, divisors. Erdős prize: no. Not yet formalized in Lean. OEIS: A002182. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_1e3cfd0dd250492e | Erdős Problem #299 has status 'disproved (lean)'. Statement: Is there an infinite sequence $a_1 < a_2 < \dots$ such that $a_{i+1} - a_i = O(1)$ and no finite sum of $\frac{1}{a_i}$ is equal to 1? There does not exist such a sequence, which follows from the positive solution to [erdosproblems.com/298] by Bloom [Bl21]. This was formalized in Lean 3 by Bloom and Mehta. Topics: number theory, unit fractions. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_1e4c48aa832b52ea | Erdős Problem #957 has been PROVED (Erdős's conjecture holds). Topics: geometry, distances. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_1e8014b7beb2ad78 | Erdős Problem #999 has been PROVED (Erdős's conjecture holds). Topics: number theory, diophantine approximation. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_1ed59bbd11466732 | Erdős Problem #813 remains OPEN. Topics: graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_1f08dd707fe4b692 | Erdős Problem #1154 has status 'not disprovable'. Topics: analysis. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_1f125ccce486db9b | Erdős Problem #1057 remains OPEN. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: A006931. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_1f1989f9e309da95 | Erdős Problem #604 remains OPEN. Topics: geometry, distances. Erdős prize: $500. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_1f3b08bef5e8ebc2 | Erdős Problem #234 remains OPEN. Statement: Is it true that for all `c ≥ 0`, the density `f c` of integers for which `(p (n + 1) - p n) / log n < c` exists and is a continuous function of `c`? Topics: number theory, primes. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_20464c19500a0724 | Erdős Problem #474 has status 'not provable'. Topics: set theory, ramsey theory. Erdős prize: $100. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_20582cd7319885d0 | Erdős Problem #223 is SOLVED. Topics: geometry, distances. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_206faae28ee79c7c | Erdős Problem #5 remains OPEN. Topics: number theory, primes. Erdős prize: no. Not yet formalized in Lean. OEIS: A001223. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_208bd134b984bc60 | Erdős Problem #1183 remains OPEN. Topics: combinatorics, ramsey theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_209da54c4ef31853 | Erdős Problem #781 has been DISPROVED (a counterexample is known). Topics: additive combinatorics. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_20a5cd5fc2edfd5e | Erdős Problem #100 remains OPEN. Statement: Is the diameter of $A$ at least $Cn$ for some constant $C > 0$? Topics: geometry, distances. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_20bb1b979b8b66c9 | Erdős Problem #420 remains OPEN. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_20c835788cca05fd | Erdős Problem #1214 has been PROVED (Erdős's conjecture holds). Statement: Let $x,y\geq 1$ be integers such that, for all $n\geq 1$, the set of primes dividing $x^{n}-1$ is equal to the set of primes dividing $y^n-1$. Must $x=y$? Erdős asked this at a 1988 number theory conference in Banff. A positive answer was given by Corrales-Rodrigáñez and Schoof [CoSc97]. Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_20dd984366cd93dd | Erdős Problem #138: machine-found Lean proof published by AlphaProof Nexus (DeepMind, arXiv 2605.22763, May 2026) (difference variant — the formalized statement is a variant, not necessarily the full original problem). Independently re-verified locally 2026-06-10: full lake build of google-deepmind/alphaproof-nexus-results@0647711a7118 under their pinned toolchain leanprover/lean4:v4.27.0 succeeded (8062 jobs); static scan clean (no sorry, no native_decide, no custom axioms). Artifacts: erdos_138.variants.difference.lean sha256:c43f8170bbf34046. AI involvement: machine-generated proof, machine-checked (Lean kernel is the referee); statement faithfulness NOT yet independently attested — see paper section 4 for DeepMind's own expert validation. | unreviewed | 0.90 | — | — | attested · 2d |
| vf_20f81fe170fe9629 | Erdős Problem #1202 is SOLVED. Topics: number theory, primes. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_21022e9a78d825a4 | Erdős Problem #1144 remains OPEN. Topics: number theory, probability. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_213c99007fd079b2 | Erdős Problem #261 remains OPEN. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_225a65a5394241cf | Erdős Problem #434 has status 'proved (lean)'. Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_230d17dc93f14212 | Erdős Problem #1205 is SOLVED. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_2329bdf075e2c6ef | Erdős Problem #617 has status 'falsifiable'. Statement: Let $r\geq 3$. If the edges of $K_{r^2+1}$ are $r$-coloured then there exist $r+1$ vertices with at least one colour missing on the edges of the induced $K_{r+1}$. In other words, there is no balanced colouring. A conjecture of Erdős and Gyárfás [ErGy99]. Topics: graph theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_2332deca7c8c4fc0 | Erdős Problem #384 has been PROVED (Erdős's conjecture holds). Topics: number theory, binomial coefficients. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_23c3d344d921ef7a | Erdős Problem #725 remains OPEN. Topics: combinatorics. Erdős prize: no. Not yet formalized in Lean. OEIS: A001009. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_23e9d5c91401383c | Erdős Problem #130 remains OPEN. Topics: graph theory, chromatic number. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_2448a611453d6052 | Erdős Problem #291 remains OPEN. Topics: number theory, unit fractions. Erdős prize: no. Not yet formalized in Lean. OEIS: A110566. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_24cf46dae6d28b1f | Erdős Problem #799 has been PROVED (Erdős's conjecture holds). Topics: graph theory, chromatic number. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_24d6e0a16126801e | Erdős Problem #791 remains OPEN. Topics: additive combinatorics. Erdős prize: no. Not yet formalized in Lean. OEIS: A066063. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_24fec59f99414222 | Erdős Problem #536 remains OPEN. Statement: Let $\epsilon>0$ and $N$ be sufficiently large. Is it true that if $A\subseteq \{1,\ldots,N\}$ has size at least $\epsilon N$ then there must be distinct $a,b,c\in A$ such that $$[a, b]=[b, c]=[a, c],$$ where $[\cdot, \cdot]$ denotes the least common multiple? Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_25181d1ebae8b85f | Erdős Problem #1059 remains OPEN. Statement: Are there infinitely many primes $p$ such that $p - k!$ is composite for each $k$ such that $1 ≤ k! < p$? Topics: number theory, primes. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A064152. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_257b2a1665aaa5d8 | Erdős Problem #808 has been DISPROVED (a counterexample is known). Topics: additive combinatorics, graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_25915d10e908fbda | Erdős Problem #516 has been PROVED (Erdős's conjecture holds). Statement: Let `f = ∑ aₖzⁿₖ` be an entire function of finite order such that `nₖ / k → ∞`. Then `limsup (fun r => ratio r f) atTop = 1`. This is proved in [Fu63]. Topics: analysis. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_25a270a415c0f9dc | Erdős Problem #312 remains OPEN. Statement: Does there exist a constant `c > 0` such that, for any `K > 1`, whenever `A` is a sufficiently large finite multiset of integers with $\sum_{n \in A} 1/n > K$ there exists some $S \subseteq A$ such that $1 - \exp(-(c*K)) < \sum_{n \in S} 1/n \le 1$? Topics: number theory, unit fractions. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_25c4ee6459b491c5 | Erdős Problem #1075 remains OPEN. Topics: hypergraphs. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_25e78cbe4f48144d | Erdős Problem #1187 is SOLVED. Topics: number theory, primes, additive combinatorics, arithmetic progressions. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_25ea90a56113f287 | Erdős Problem #900 has been PROVED (Erdős's conjecture holds). Topics: graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_25ed110668570c6f | Erdős Problem #428 remains OPEN. Statement: Is there a set $A\subseteq \mathbb{N}$ such that, for infinitely many $n$, all of $n-a$ are prime for all $a\in A$ with $0 < a < n$ and $$\liminf\frac{\lvert A\cap [1,x]\rvert}{\pi(x)}>0?$$ Topics: number theory, primes. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_25ef36d5afd13aa7 | Erdos-Heilbronn conjecture (1964, solved 1996 by Dias da Silva and Hamidoune): for a prime p and a subset A of Z/pZ, the cardinality of the restricted sumset A +_hat A is at least min(p, 2|A| - 3). | unreviewed | 0.95 | — | — | asserted · 13d |
| vf_2612de4a4f57659e | Erdős Problem #864 remains OPEN. Topics: number theory, sidon sets, additive combinatorics. Erdős prize: no. Not yet formalized in Lean. OEIS: A389182. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_2685ff832f805e02 | Erdős Problem #993 has status 'falsifiable'. Topics: graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_268fcebae708a61c | Erdős Problem #479 remains OPEN. Statement: Is it true that, for all $k\neq 1$, there are infinitely many $n$ such that $2^n\equiv k\pmod{n}$? Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A036236, A015919, A050259, A015921, A006521, A006517, A015940. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_26d6a4903f53badd | Erdős Problem #400 remains OPEN. Topics: number theory, factorials. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_26e65a6dc2cca455 | Erdős Problem #97 has status 'falsifiable'. Statement: Does every convex polygon have a vertex with no other 4 vertices equidistant from it? Topics: geometry, distances, convex. Erdős prize: $100. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_272296e167402b91 | Erdős Problem #528 remains OPEN. Topics: geometry. Erdős prize: no. Not yet formalized in Lean. OEIS: A387897, A156816. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_275f1cae949d16b3 | Erdős Problem #715 has been PROVED (Erdős's conjecture holds). Topics: graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_27976ae88f33a208 | Erdős Problem #968 remains OPEN. Statement: Does the set `{n | u n < u (n+1)}` have positive natural density? Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A387591. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_279c39771cc33ddf | Erdős Problem #585 remains OPEN. Topics: graph theory, cycles. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_279e997d3b3da2ee | OBLIGATION (Erdos #1093). BANKED: three delta=1 examples beyond ELS93 (k=106/126/129) verified; the density model leans finite. OPEN: prove finiteness of the delta=1 deficiency cases (the density argument is heuristic, not a proof). | unreviewed | 0.50 | — | — | asserted · 2d |
| vf_28330b3ec4ac8914 | Erdős Problem #34 has status 'disproved (lean)'. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: A389241, A234813, A390187. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_28597cc210f7745b | Erdős Problem #1061 remains OPEN. Statement: How many (ordered) solutions are there to `σ(a) + σ(b) = σ(a + b)` with `a + b ≤ x`? Is it true that this number is asymptotic to `c * x` for some constant `c > 0`? Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A110177, possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_2862431b0c7ff63a | Erdős Problem #1115 is SOLVED. Topics: analysis. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_2883600ce8715267 | Erdős Problem #1132 remains OPEN. Topics: analysis, polynomials. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_289a29b7f1007749 | Erdős Problem #459 has status 'solved (lean)'. Topics: number theory, primes. Erdős prize: no. Not yet formalized in Lean. OEIS: A289280. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_289bf805554e9675 | Erdős Problem #58 has been PROVED (Erdős's conjecture holds). Topics: graph theory, chromatic number, cycles. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_292924b560a030f2 | Erdős Problem #545 remains OPEN. Topics: graph theory, ramsey theory. Erdős prize: no. Not yet formalized in Lean. OEIS: A059442, possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_2940c66854443a62 | Erdős Problem #325 remains OPEN. Statement: Writing $f_{k, 3}(x)$ for the number of integers $\leq x$ which are the sum of three $k$th powers, is it true that $f_{k, 3}(x) \gg x ^ (3 / k)$? Topics: number theory, powers. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_29ab904190a2f3db | Erdős Problem #139 has been PROVED (Erdős's conjecture holds). Statement: **Erdős Problem 139**: Let $r_k(N)$ be the size of the largest subset of ${1,...,N}$ which does not contain a non-trivial $k$-term arithmetic progression. Prove that $r_k(N) = o(N)$. Topics: additive combinatorics, arithmetic progressions. Erdős prize: $1000. Statement is machine-verified in Lean (formal-conjectures). OEIS: A003002, A003003, A003004, A003005. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_29c8b747d0aa12af | Erdős Problem #488 has status 'falsifiable'. Statement: Let $A$ be a finite set and $$B=\{ n \geq 1 : a\mid n\textrm{ for some }a\in A\}.$$ Is it true that, for every $m>n\geq \max(A)$, $$\frac{\lvert B\cap [1,m]\rvert }{m}< 2\frac{\lvert B\cap [1,n]\rvert}{n}?$$ Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_29c94ce4f019a8e0 | Erdős Problem #520 remains OPEN. Statement: Let $f$ be a Rademacher multiplicative function. Does there exist some constant $c > 0$ such that, almost surely, $$ \limsup_{N \to \infty} \frac{\sum_{m \leq N} f(m)}{\sqrt{N \log \log N}} = c? $$ Topics: number theory, probability. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_29e57f0bb3cb3126 | Erdős Problem #134 has status 'proved (lean)'. Topics: graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_2a5f61af4739089c | Erdős Problem #800 has been PROVED (Erdős's conjecture holds). Topics: graph theory, ramsey theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_2a7b7c98a289ec00 | Erdős Problem #1086 remains OPEN. Topics: geometry, distances. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_2aacd8605d588b53 | Erdős Problem #1006 has been DISPROVED (a counterexample is known). Topics: graph theory, cycles. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_2b1aac0def0b93da | Erdős Problem #383 remains OPEN. Statement: Is it true that for every $k$ there are infinitely many primes $p$ such that the largest prime divisor of $$ \prod_{i = 0}^k (p ^ 2 + i) $$ is $p$? Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_2b1d432fcb715fd3 | The Erdős Problems database at erdosproblems.com catalogs problems posed by or jointly attributed to Paul Erdős, with public status (open, partial, solved) and citations to the original problem statement. | unreviewed | 0.30 | — | — | asserted · 4w |
| vf_2b8489ebb91da51e | Erdős Problem #425 remains OPEN. Topics: number theory, sidon sets. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_2b98b0ec9462e617 | Erdős Problem #1008 has status 'proved (lean)'. Topics: graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_2bbe2e07295e7b2e | Erdős Problem #1065 remains OPEN. Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A074781, A339465. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_2bd0397eda13ccde | Sunflower lemma improvement (Erdos-Ko 1960 conjecture; Alweiss-Lovett-Wu-Zhang 2020 partial resolution): every family of k-element sets of size at least (C log k)^k contains a sunflower of size r, where the bound (k!)^r in the original Erdos-Ko 1960 lemma improves dramatically. Original conjecture open at the C^k bound. | unreviewed | 0.85 | — | — | asserted · 13d |
| vf_2bf7b3ced93c8c66 | Erdős Problem #379 has status 'proved (lean)'. Statement: Let $S(n)$ denote the largest integer such that, for all $1 ≤ k < n$, the binomial coefficient $\binom{n}{k}$ is divisible by $p^S(n)$ for some prime $p$ (depending on $k$).Then $\limsup S(n) = \infty$. This was formalized in Lean by Tao. Topics: number theory, binomial coefficients. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_2c10149e5fdf00fc | Erdős Problem #259 has status 'proved (lean)'. Statement: Is $\sum_{n} \mu(n)^2\frac{n}{2^n}$ irrational? This is true, and was proved by Chen and Ruzsa. [ChRu99] Chen, Yong-Gao and Ruzsa, Imre Z., On the irrationality of certain series. Period. Math. Hungar. (1999), 31--37. Topics: irrationality. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A371134. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_2c6965f2c81d49f6 | Erdős Problem #250 has been PROVED (Erdős's conjecture holds). Statement: Is $$ \sum_{n=1}^\infty \frac{\sigma(n)}{2^n} $$ irrational? Here $\sigma(n)$ is the sum of divisors function. The answer is yes, as shown by Nesterenko [Ne96]. [Ne96] Nesterenko, Yu V., _Modular functions and transcendence questions_, Mat. Sb. 187 *9* (1996), 1319--1348. Topics: number theory, irrationality. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A066766. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_2c6d3c9f87b43ccd | Erdős Problem #489 remains OPEN. Statement: Let $A\subseteq \mathbb{N}$ be a set such that $\lvert A\cap [1,x]\rvert=o(x^{1/2})$. Let $B=\{ n\geq 1 : a\nmid n\textrm{ for all }a\in A\}$. If $B=\{b_1 < b_2 < \cdots\}$ then is it true that $$\lim_{x \to \infty} \frac{1}{x}\sum_{b_i < x}(b_{i+1}-b_i)^2$$ exists (and is finite)? For example, when $A=\{p^2: p\textrm{ prime}\}$ then $B$ is the set of squarefree numbers, and the existence of this limit was proved by Erdős. See also [208]. Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_2c7d9bb89ca1e804 | Erdős Problem #843 has been PROVED (Erdős's conjecture holds). Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_2ce0a45e23ece2cf | Erdős Problem #174 remains OPEN. Topics: geometry, ramsey theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_2cfc468cd4150cdc | Erdős Problem #228 has been PROVED (Erdős's conjecture holds). Statement: Does there exist, for all large $n$, a polynomial $P$ of degree $n$, with coefficients $\pm1$, such that $$\sqrt n \ll |P(z)| \ll \sqrt n$$ for all $|z|=1$, with the implied constants independent of $z$ and $n$? The answer is yes, proved by Balister, Bollobás, Morris, Sahasrabudhe, and Tiba [BBMST19]. [BBMST19] Balister, P. and Bollob\'{A}s, B. and Morris, R. and Sahasrabudhe, J. and Tiba, M., _Flat Littlewood Polynomials Exist_. arXiv:1907.09464 (2019). Topics: analysis, polynomials. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_2d14f09def3cdde1 | Erdős Problem #276 remains OPEN. Statement: Is there an infinite Lucas sequence $a_0, a_1, \ldots$ where $a_{n+2} = a_{n+1} + a_n$ for $n \ge 0$ such that all $a_k$ are composite, and yet no integer has a common factor with every term of the sequence? Topics: number theory, covering systems. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_2d42c8a77bd89b44 | Erdős Problem #561 remains OPEN. Topics: graph theory, ramsey theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_2d4edfce58578092 | OBLIGATION (Erdos #1094). BANKED: the 14 ELS exceptions enumerated provably-complete to k<=40 (binom_exception_enum). OPEN: extend the complete enumeration / prove finiteness of the exception set for all k. | unreviewed | 0.50 | — | — | asserted · 2d |
| vf_2d68ab9151b52c16 | Erdős Problem #637 has been PROVED (Erdős's conjecture holds). Topics: graph theory, ramsey theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_2d9460662bd45612 | Erdős Problem #889 remains OPEN. Statement: Let $v(n,k)$ count the prime factors of $n+k$ which do not divide $n+i$ for $0\leq i < k$. Is it true that $v_0(n)=\max_{k\geq 0}v(n,k)\to \infty$ as $n\to \infty$? Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_2dae0f3b07e2ecfa | Erdős Problem #803 has been DISPROVED (a counterexample is known). Topics: graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_2db3437d1512c222 | OBLIGATION (Erdos #700). BANKED: f(n)=min gcd(n,C(n,k)) recomputed for the cited cases (semiprime and prime-power families). OPEN: characterize f(n) in general beyond the verified families. | unreviewed | 0.50 | — | — | asserted · 2d |
| vf_2db84fc2e06da52e | Erdős Problem #1027 has been PROVED (Erdős's conjecture holds). Topics: combinatorics. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_2dd664c8e28d82d0 | Erdős Problem #747 is SOLVED. Topics: combinatorics, hypergraphs. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_2ddacec05f44f923 | Erdős Problem #620 remains OPEN. Topics: graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_2de03f410f195cdc | Erdős Problem #32 remains OPEN. Statement: Does there exist a set $A \subseteq \mathbb{N}$ such that $|A \cap \{1, \ldots, N\}| = o((\log N)^2)$ and every sufficiently large integer can be written as $p + a$ for some prime $p$ and $a \in A$? Topics: number theory, additive basis. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_2e71ab39981ba1fa | Erdős Problem #974 has status 'proved (lean)'. Topics: analysis. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_2ecfa815bd38b0ce | Erdős Problem #1109 remains OPEN. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: A392164, A392165. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_2f0ecec49cc6e102 | Erdős Problem #895 has been PROVED (Erdős's conjecture holds). Topics: additive combinatorics, graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_2f358948da97e0d6 | Erdős Problem #1063 remains OPEN. Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A389360. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_2f3c732563c66789 | Erdős Problem #959 remains OPEN. Topics: geometry, distances. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_2f7f52ccca0a343f | Erdős Problem #692 has status 'disproved (lean)'. Topics: number theory, divisors. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_30e78fa94c9ad0eb | Erdős Problem #107 has status 'falsifiable'. Statement: Let $f(n)$ be minimal such that any $f(n)$ points in $ℝ^2$, no three on a line, contain $n$ points which form the vertices of a convex $n$-gon. Prove that $f(n) = 2^{n-2} + 1$. Topics: geometry, convex. Erdős prize: $500. Statement is machine-verified in Lean (formal-conjectures). OEIS: A000051. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_31c1bdafd36dbad5 | Erdős Problem #631 has been PROVED (Erdős's conjecture holds). Topics: graph theory, chromatic number. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_3212ff88ecf489e9 | Erdős Problem #798 has status 'proved (lean)'. Topics: geometry. Erdős prize: no. Not yet formalized in Lean. OEIS: A116446. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_3273d65fd327cf4d | Erdős Problem #1201 remains OPEN. Topics: number theory, primes. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_327a08af5b534f4d | Erdős Problem #1021 has been PROVED (Erdős's conjecture holds). Topics: graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_32858694abf43cb8 | Erdős Problem #54 is SOLVED. Topics: number theory, ramsey theory. Erdős prize: $100. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_33097d9535ebf13d | Erdős Problem #15 remains OPEN. Statement: Is it true that $\sum_{n=1}^\infty(-1)^n\frac{n}{p_n}$ converges, where $p_n$ is the sequence of primes? Note: In the problem statement, $p_n$ is the $n$-th prime, indexed such that $p_1=2, p_2=3, \ldots$. We 0-index here to reflect how Nat.nth works. Topics: number theory, primes. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_33a92fa5d3b28d96 | Erdős Problem #905 has status 'proved (lean)'. Topics: graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_33aba114a507abf5 | Erdős Problem #46 has status 'proved (lean)'. Topics: number theory, unit fractions, ramsey theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_33f5a809ba6ed690 | Erdős Problem #304 remains OPEN. Topics: number theory, unit fractions. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A097847, A097849. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_341620e026d9a573 | Erdős Problem #771 has been PROVED (Erdős's conjecture holds). Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_345e7e59ef1192a4 | Erdős Problem #369 has status 'proved (lean)'. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_3479148779caba72 | Erdős Problem #594 has been PROVED (Erdős's conjecture holds). Topics: graph theory, set theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_349a8a24fe2c5b0d | Erdős Problem #427 has status 'proved (lean)'. Statement: **Erdős Problem 427**: is it true that, for every $n$ and $d$, there exists $k$ such that $$ d \mid p_{n + 1} + \cdots + p_{n + k}, $$ where $p_r$ denotes the $r$th prime? Topics: number theory, primes. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_34ad4a68cd3dca8b | Erdős Problem #976 remains OPEN. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_34e3c64c8b737a35 | Erdős Problem #505 has status 'disproved (lean)'. Statement: **Erdős Problem 505** (disproved). Borsuk's conjecture is false for sufficiently large $n$: there exists a dimension $n$ and a bounded set $S \subseteq \mathbb{R}^n$ with positive diameter such that $S$ cannot be covered by $n + 1$ subsets each of diameter strictly less than $\operatorname{diam}(S)$. Erdős [Er44] suspected this. Disproved by Kahn–Kalai [KK93] for $n \geq 2015$. Currently known to be false for $n \geq 64$. A formal proof was formalised by Boris Alexeev using Aristotle. Topics: geometry. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_35005d1cee601049 | Erdős Problem #450 remains OPEN. Topics: number theory, divisors. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_358dd9a94380e60d | Erdős Problem #1068 remains OPEN. Statement: Does every graph with chromatic number $\aleph_1$ contain a countable subgraph which is infinitely connected? Topics: graph theory, set theory, chromatic number. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_3593b55c707888a0 | Erdős Problem #857 remains OPEN. Statement: Estimate `m(n,k)`, or better give an asymptotic formula. Topics: combinatorics. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_359c6e30cd652e65 | Erdős Problem #376 remains OPEN. Statement: Are there infinitely many $n$ such that ${2n\choose n}$ is coprime to $105$? Topics: number theory, binomial coefficients, base representations. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A030979. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_35ad08b7f532ef7f | Erdős Problem #920 remains OPEN. Statement: Is it true that, for $k\geq 4$, $f_k(n) \gg \frac{n^{1-\frac{1}{k-1}}}{(\log n)^{c_k}}$ for some constant $c_k>0$? Topics: graph theory, chromatic number. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_35ee241deaf2a434 | Erdős Problem #729 has status 'proved (lean)'. Topics: number theory, factorials. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_363727eeef8ebd87 | Erdős Problem #121 has been DISPROVED (a counterexample is known). Topics: number theory, squares. Erdős prize: no. Not yet formalized in Lean. OEIS: A028391, A013928, A372306, A373319, A372306, A373178, A360659, A373114, A143301. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_36820729a6cf72aa | Erdős Problem #2 has been DISPROVED (a counterexample is known). Topics: number theory, covering systems. Erdős prize: $1000. Not yet formalized in Lean. OEIS: A160559. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_36b6fbe159d767bd | Erdős Problem #601 remains OPEN. Topics: graph theory, set theory. Erdős prize: $500. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_36f6ca019d9464b8 | Erdős Problem #290 has status 'proved (lean)'. Topics: number theory, unit fractions. Erdős prize: no. Not yet formalized in Lean. OEIS: A375081. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_373bfdb5682a1918 | Erdős Problem #402 has been PROVED (Erdős's conjecture holds). Statement: Prove that, for any finite set $A\subset\mathbb{N}$, there exist $a, b\in A$ such that $$ \gcd(a, b)\leq a/|A|. $$ Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_377ba211ef539d40 | Erdős Problem #16 has status 'disproved (lean)'. Statement: Is the set of odd integers not of the form $2^k+p$ the union of an infinite arithmetic progression and a set of density $0$? Erdős called this conjecture "rather silly". Chen [Ch23] has proved the answer is no. This was formalized in Lean by Chin using Aristotle. Topics: number theory, additive basis, primes. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A006285. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_378080975f8c6eea | Erdős Problem #1158 remains OPEN. Topics: hypergraphs, turan number. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_37b1410062dbcbdf | Erdős Problem #1213 has been PROVED (Erdős's conjecture holds). Topics: additive combinatorics. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_38886e82d5896200 | Erdős Problem #218 remains OPEN. Topics: number theory, primes. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A333230, A333231, A064113. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_394c360cf3eca953 | Erdős Problem #710 remains OPEN. Topics: number theory. Erdős prize: ₹2000. Not yet formalized in Lean. OEIS: A390246. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_3965aaa612abfacd | Erdős Problem #160 remains OPEN. Topics: additive combinatorics, arithmetic progressions. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_39851498975f7667 | Erdős Problem #1062 remains OPEN. Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A038372. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_398a9208a3bc626b | Erdős Problem #818 has status 'proved (lean)'. Topics: additive combinatorics. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_398ab61b5ce69b48 | Erdős Problem #513 remains OPEN. Statement: Let `f` be a transcendental entire function. What is the greatest possible value of `liminf (fun r : ℝ => ratio r f) atTop`? Topics: analysis. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_39bada7eab345ace | Erdős Problem #135 has been DISPROVED (a counterexample is known). Topics: distances, geometry. Erdős prize: $250. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_39bea67f4eee3435 | Erdős Problem #82 remains OPEN. Statement: $F(n) / \log n \to \infty as n \to \infty$ Topics: graph theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A120414, A390256, A390257, A390919, A392636, A394400, A394462, A394539, A394563, A394564, A394573, A394574, A394930, A394933. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_39c2a827b85e3ebf | Erdős Problem #1034 has status 'disproved (lean)'. Topics: graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_3aaf350b30f0781f | Erdős Problem #356 has been PROVED (Erdős's conjecture holds). Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_3ac45f9da74cfe24 | Erdős Problem #238 remains OPEN. Statement: Let `c₁, c₂ > 0`. Is it true that for any sufficiently large `x`, there exists more than `c₁ * log x` many consecutive primes `≤ x` such that the difference between any two is `> c₂`? Topics: number theory, primes. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_3b9b3f6ad700cb91 | Erdős Problem #315 has status 'proved (lean)'. Topics: number theory, unit fractions. Erdős prize: no. Not yet formalized in Lean. OEIS: A000058, A076393. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_3ba117991ee7046f | Erdős Problem #928 remains OPEN. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: A006530. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_3bc7d9c07a1c8452 | Erdős Problem #11 remains OPEN. Statement: Is every odd $n > 1$ the sum of a squarefree number and a power of 2? Topics: number theory, additive basis. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A001220, A377587. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_3bdeedd439e228be | Erdős Problem #347 has status 'proved (lean)'. Statement: Is there a sequence $A=\{a_1\leq a_2\leq \cdots\}$ of integers with $$\lim \frac{a_{n+1}}{a_n}=2$$ such that $$P(A')= \left\{\sum_{n\in B}n : B\subseteq A'\textrm{ finite }\right\}$$ has density $1$ for every cofinite subsequence $A'$ of $A$? This has been solved in the affirmative by ebarschkis in the comments (based on idea of Tao and van Doorn, also in the comments). Thos was formalized in Lean by Barschkis using Aristotle. Topics: number theory, complete sequences. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_3be126b722c65b30 | Erdős Problem #664 has been DISPROVED (a counterexample is known). Topics: combinatorics. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_3be6fbb0bb72199c | Erdős Problem #598 remains OPEN. Statement: **Erdős Problem 598:** Let $m$ be an infinite cardinal and $\kappa$ be the successor cardinal of $2^{\aleph_0}$. Can one colour the countable subsets of $m$ using $\kappa$ many colours so that every $X \subseteq m$ with $|X| = \kappa$ contains subsets of all possible colours? Topics: set theory, ramsey theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_3c46f7ac6d33bb43 | Erdős Problem #1013 remains OPEN. Topics: graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: A292528. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_3caaec8573ea8c65 | Erdős Problem #1181 remains OPEN. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_3cb60f7e78e8d27f | Erdős Problem #706 remains OPEN. Topics: graph theory, chromatic number. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_3ce70dd04e1c7636 | Erdős Problem #1029 remains OPEN. Topics: graph theory, ramsey theory. Erdős prize: $100. Not yet formalized in Lean. OEIS: A059442. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_3dd39b42134be1b2 | Erdős Problem #84 remains OPEN. Topics: graph theory, cycles. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_3e30d376c9e0d7f7 | Erdős Problem #770 remains OPEN. Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A263647, possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_3e5db1b1d8c3abe1 | Erdős Problem #1190 has status 'solved (lean)'. Topics: number theory, covering systems. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_3e6b704c6393a971 | Erdős Problem #437 has been PROVED (Erdős's conjecture holds). Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_3e7dea78f30ae1e8 | Erdős Problem #111 remains OPEN. Topics: graph theory, chromatic number, set theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_3ec8d05585f676ec | Erdős Problem #166 has been PROVED (Erdős's conjecture holds). Topics: graph theory, ramsey theory. Erdős prize: $250. Not yet formalized in Lean. OEIS: A059442. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_3ecc100261603880 | Erdős Problem #126 remains OPEN. Statement: Let $f(n)$ be maximal such that if $A\subseteq\mathbb{N}$ has $|A| = n$ then $\prod_{a\neq b\in A}(a + b)$ has at least $f(n)$ distinct prime factors. Is it true that $\frac{f(n)}{\log n} \to\infty$? Topics: number theory. Erdős prize: $250. Statement is machine-verified in Lean (formal-conjectures). OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_3ecdb02a421a10b3 | Erdős Problem #555 remains OPEN. Topics: graph theory, ramsey theory. Erdős prize: no. Not yet formalized in Lean. OEIS: A389313, possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_3f336c8c039c0031 | Erdős Problem #810 remains OPEN. Topics: graph theory, ramsey theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_3f3bfd9b358fec1d | Erdős Problem #1152 remains OPEN. Topics: analysis, polynomials. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_3f7f35489d6f3981 | Erdős Problem #213 remains OPEN. Statement: Let $n \geq 4$. Are there $n$ points in $\mathbb{R}^2$, no three on a line and no four on a circle, such that all pairwise distances are integers? Topics: geometry, distances. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_3f89f6688f969003 | Erdős Problem #451 remains OPEN. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: A386620. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_3fb0f12f82f934b6 | Erdős Problem #1046 has been DISPROVED (a counterexample is known). Topics: analysis. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_3fbb4b71ba598958 | Erdős Problem #575 remains OPEN. Topics: graph theory, turan number. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_3fda07b7cb168e7b | Erdős Problem #755 has been PROVED (Erdős's conjecture holds). Topics: geometry. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_4085bc6502fae2cd | Erdős Problem #961 remains OPEN. Statement: It is conjectured that $f(k) \ll (\log k)^O(1)$. Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A213253. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_40f5d55d40f160b5 | Erdős Problem #1049 remains OPEN. Statement: Let $t>1$ be a rational number. Is $\sum_{n=1}^\infty\frac{1}{t^n-1}=\sum_{n=1}^\infty \frac{\tau(n)}{t^n}$ irrational, where $\tau(n)$ counts the divisors of $n$? A conjecture of Chowla. Topics: irrationality. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_41180c4873c1c6da | Erdős Problem #210 has been PROVED (Erdős's conjecture holds). Topics: geometry. Erdős prize: no. Not yet formalized in Lean. OEIS: A003034. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_41284d5868c13c2d | Erdős Problem #242 has status 'falsifiable'. Statement: For every $n>2$ there exist distinct integers $1 ≤ x < y < z$ such that $\frac 4 n = \frac 1 x + \frac 1 y + \frac 1 z$. Topics: number theory, unit fractions. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A073101, A075245, A075246, A075247, A075248, A287116. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_4178d989faad6623 | Erdős Problem #23 has status 'falsifiable'. Statement: Can every triangle-free graph on $5n$ vertices be made bipartite by deleting at most $n^2$ edges? Topics: graph theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A389646. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_42044e41a4763482 | Erdős Problem #171 has been PROVED (Erdős's conjecture holds). Topics: additive combinatorics, combinatorics. Erdős prize: no. Not yet formalized in Lean. OEIS: A156989. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_42119421374bd647 | Erdős Problem #723 has status 'falsifiable'. Statement: If there is a finite projective plane of order $n$ then must $n$ be a prime power? Topics: combinatorics. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_4218893cd9de44fe | Erdős Problem #718 has been PROVED (Erdős's conjecture holds). Topics: graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_4241bafea0a9562d | Erdős Problem #432 remains OPEN. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_429a5477849e42ca | Erdős Problem #367 remains OPEN. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: A057521. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_42d8a30e5eb53325 | Erdős Problem #1180 has been PROVED (Erdős's conjecture holds). Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_42f67e4605225d1b | Erdős Problem #1020 has status 'falsifiable'. Topics: graph theory, hypergraphs. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_43954aa3edf301fe | Erdős Problem #554 remains OPEN. Topics: graph theory, ramsey theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_43cfda269c85ec0c | Erdős Problem #518 has been PROVED (Erdős's conjecture holds). Topics: graph theory, ramsey theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_440e0cf1ae712d54 | Erdős Problem #484 has status 'proved (lean)'. Topics: number theory, additive combinatorics, ramsey theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_442ca909634589c8 | Erdős Problem #707 has status 'disproved (lean)'. Statement: **Erdős Problem 707**: It is false that any finite Sidon set can be embedded in a perfect different set modulo some $n$. As described in [arxiv/2510.19804], a counterexample is provided in [Ha47], see below. The proof of this has been formalized. This was formalized in Lean by Alexeev using ChatGPT. Topics: additive combinatorics, sidon sets. Erdős prize: $1000. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_443ab1ef1d327cbf | Erdős Problem #761 remains OPEN. Topics: graph theory, chromatic number. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_443e458aafef6234 | Erdős Problem #1038 remains OPEN. Topics: analysis. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_44a9725ec2fa08e4 | Erdős Problem #901 remains OPEN. Topics: combinatorics, hypergraphs. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_44ac7955da520c98 | Erdős Problem #697 has been PROVED (Erdős's conjecture holds). Topics: number theory, divisors. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_44d3d012a6289ebb | Erdős Problem #621 has status 'proved (lean)'. Topics: graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_45074989f099dc09 | Erdős Problem #605 has been PROVED (Erdős's conjecture holds). Topics: geometry, distances. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_4515c4abc7c4db0f | Erdős Problem #1124 has been PROVED (Erdős's conjecture holds). Topics: geometry. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_454f012e0205fa67 | Erdős Problem #17 remains OPEN. Statement: **Erdős Problem 17.** Are there infinitely many cluster primes? Topics: number theory, primes. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A038133. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_456e0ee6a09a85c7 | Erdős Problem #760 has status 'proved (lean)'. Topics: graph theory, chromatic number. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_4599cc6c9a4e4b14 | Erdős Problem #849 remains OPEN. Statement: Is it true that, for every integer $t\geq1$, there is some integer $a$ such that ${n \choose k} = a$ with $1\leq k \le \frac{n}{2}$ has exactly $t$ solutions? Topics: number theory, binomial coefficients. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A003016, A003015, A059233, A098565, A090162, A180058, A182237. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_45b7d3a8881c9fa6 | Erdős Problem #1161 is SOLVED. Topics: group theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_45d635e6794b5137 | Erdős Problem #487 has status 'proved (lean)'. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_4684fa7570ddaf6f | Erdős Problem #831 remains OPEN. Topics: geometry. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_468e19523dbf2d1c | Erdős Problem #1215 has been DISPROVED (a counterexample is known). Topics: analysis. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_46be6caf54438abe | Erdős Problem #955 remains OPEN. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_472afab786f5d922 | Erdős Problem #558 remains OPEN. Topics: graph theory, ramsey theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_475101d8dc64f3b4 | Erdős Problem #42 has status 'solved (lean)'. Statement: **Erdős Problem 42**: Let M ≥ 1 and N be sufficiently large in terms of M. Is it true that for every maximal Sidon set `A ⊆ {1,…,N}` there is another Sidon set `B ⊆ {1,…,N}` of size M such that `(A - A) ∩ (B - B) = {0}`? This was proved for all $M$ by GPT 5.5 Pro (prompted by Sandhu), see discussion thread for more details. Topics: number theory, sidon sets, additive combinatorics. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_4783dd0612b705fb | Erdős Problem #267 remains OPEN. Statement: Let $F_1=F_2=1$ and $F_{n+1} = F_n + F_{n-1}$ be the Fibonacci sequence. Let $n_1 < n_2 < \dots$ be an infinite sequence with $\frac{n_{k+1}}{n_k} \ge c > 1$. Must $\sum_k \frac 1 {F_{n_k}}$ be irrational? Topics: irrationality. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_47df26477095f3e8 | Erdős Problem #776 remains OPEN. Topics: combinatorics. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_484ed714dba000f6 | Erdős Problem #398 has status 'falsifiable'. Statement: **Brocard's Problem** Does $n! + 1 = m^2$ have integer solutions other than $n = 4, 5, 7$? Topics: number theory, factorials. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A146968, A141399. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_488d07d058d4ffe9 | Erdős Problem #590 has been PROVED (Erdős's conjecture holds). Statement: Let $α$ be the infinite ordinal $\omega^{\omega}$. It was proved by Chang [Ch72] that any red/blue colouring of the edges of $K_α$ there is either a red $K_α$ or a blue $K_3$. Topics: set theory, ramsey theory. Erdős prize: $250. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_488d32b13bdf7892 | Erdős Problem #705 has been DISPROVED (a counterexample is known). Statement: Let $G$ be a finite unit distance graph in $\mamthbb{R}^2$. Is there some $k$ such that if $G$ has girth $≥ k$, then $\chi(G) ≤ 3$? The general case was solved by O'Donnell [OD99], who constructed finite unit distance graphs with chromatic number $4$ and arbitrarily large girth. Topics: graph theory, chromatic number. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_4897356e1b62b9d0 | Erdős Problem #671 remains OPEN. Topics: analysis. Erdős prize: $250. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_494a17bb46d53c8c | Erdős Problem #60 remains OPEN. Topics: graph theory, cycles. Erdős prize: no. Not yet formalized in Lean. OEIS: A006855. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_49b48e8820c6ff1d | Erdős Problem #1009 has been PROVED (Erdős's conjecture holds). Topics: graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_4b47b99524e8c7e9 | Erdős Problem #1157 remains OPEN. Topics: hypergraphs, turan number. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_4be95d2df14f26a5 | Erdős Problem #397 has status 'disproved (lean)'. Statement: Are there only finitely many solutions to $$ \prod_i \binom{2m_i}{m_i}=\prod_j \binom{2n_j}{n_j} $$ with the $m_i,n_j$ distinct? Somani, using ChatGPT, has given a negative answer. In fact, for any $a\geq 2$, if $c=8a^2+8a+1$, $\binom{2a}{a}\binom{4a+4}{2a+2}\binom{2c}{c}= \binom{2a+2}{a+1}\binom{4a}{2a}\binom{2c+2}{c+1}.$ Further families of solutions are given in the comments by SharkyKesa. This was earlier asked about in a [MathOverflow] question, in response to which Elkies also gave an alternative construction which produces solutions - at the moment it is not clear whether Elkies' argument gives infinitely many solutions (although Bloom believes that it can). This was formalized in Lean by Wu using Aristotle. Topics: number theory, binomial coefficients. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_4bec230d5f70b872 | Erdős Problem #871 has status 'disproved (lean)'. Topics: number theory, additive basis. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_4c16b68f1e3caa7c | Erdős Problem #503 remains OPEN. Statement: What is the size of the largest $A \subseteq \mathbb{R}^n$ such that every three points from $A$ determine an isosceles triangle? That is, for any three points $x$, $y$, $z$ from $A$, at least two of the distances $|x - y|$, $|y - z|$, $|x - z|$ are equal. Topics: geometry, distances. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A175769. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_4c2d179f306ff3fd | Erdős Problem #339 has been PROVED (Erdős's conjecture holds). Topics: number theory, additive basis. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_4c98f77d6dcdb7f8 | Erdős Problem #648 has status 'solved (lean)'. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: A391750. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_4ca4215e2e87ae83 | Erdős Problem #1031 has been PROVED (Erdős's conjecture holds). Topics: graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_4cca1a35c234d083 | Erdős Problem #687 remains OPEN. Topics: number theory. Erdős prize: $1000. Not yet formalized in Lean. OEIS: A048670, A058989. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_4cd4571fc1beca1b | Erdős Problem #834 is SOLVED. Topics: graph theory, hypergraphs. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_4d7d3f696bc384b6 | Erdős Problem #1197 has status 'disproved (lean)'. Topics: analysis. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_4dc9ff21209305c5 | Erdős Problem #320 remains OPEN. Topics: number theory, unit fractions. Erdős prize: no. Not yet formalized in Lean. OEIS: A072207. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_4e5ba79ba48b35b1 | Erdős Problem #736 has status 'not provable'. Topics: graph theory, chromatic number. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_4e613de8e4f4dcc5 | Erdős Problem #1050 has been PROVED (Erdős's conjecture holds). Topics: irrationality. Erdős prize: no. Not yet formalized in Lean. OEIS: A331372. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_4ea4e7224209bddd | Erdős Problem #232 has been PROVED (Erdős's conjecture holds). Topics: geometry, distances. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_4f17d23fae870532 | Erdős Problem #1073 remains OPEN. Statement: Is it true that $A(x) \le x^{o(1)}$? Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A256519. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_4f7023228c907a9d | Erdős Problem #287 has status 'falsifiable'. Topics: number theory, unit fractions. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_4fb2eda9585453b2 | Erdős Problem #734 remains OPEN. Topics: combinatorics. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_4fd61820b78bdedf | Erdős Problem #204 has status 'disproved (lean)'. Statement: Are there $n$ such that there is a covering system with moduli the divisors of $n$ which is 'as disjoint as possible'? That is, for all $d\mid n$ with $d>1$ there is an associated $a_d$ such that every integer is congruent to some $a_d\pmod{d}$, and if there is some integer $x$ with $$x\equiv a_d\pmod{d}\textrm{ and }x\equiv a_{d'}\pmod{d'}$$then $(d,d')=1$. The density of such $n$ is zero. Erdős and Graham believed that no such $n$ exist. Adenwalla [Ad25] has proved there are no such $n$. This was formalized by van Doorn in Lean using Aristotle. Topics: covering systems. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_4fec4a78d574b4f4 | Erdős Problem #153 remains OPEN. Statement: Must `lim f n = ∞`? Topics: sidon sets. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_4ffc29ddfbf57061 | Erdős Problem #654 remains OPEN. Topics: geometry, distances. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_5060a1f3f42fce75 | Erdős Problem #80 remains OPEN. Topics: graph theory, ramsey theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_506c9a7b5f6f36b4 | Erdős Problem #460 remains OPEN. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_507e61fe107d57bb | Erdős Problem #377 remains OPEN. Statement: Is there some absolute constant $C > 0$ such that $$ \sum_{p \leq n} 1_{p\nmid {2n \choose n}}\frac{1}{p} \leq C $$ for all $n$? Topics: number theory, binomial coefficients. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_5087d18c57648083 | Erdős Problem #159 remains OPEN. Topics: graph theory, ramsey theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_509064665add1912 | Erdős Problem #1039 remains OPEN. Topics: analysis. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_50d220a3d1efb2eb | Erdős Problem #848 has status 'decidable'. Statement: Is the maximum size of a set $A ⊆ \{1, \dots, N\}$ such that $ab + 1$ is never squarefree (for all $a, b ∈ A$) achieved by taking those $n ≡ 7 \pmod{25}$? This asks whether `Erdos848 N` holds for all $N$ (formulated using `A ⊆ Finset.range N`). This was solved for all sufficiently large $N$ by Sawhney in this note. In fact, Sawhney proves something slightly stronger, that there exists some constant $c>0$ such that if $\lvert A\rvert \geq (\frac{1}{25}-c)N$ and $N$ is large then $A$ is contained in either $\{ n\equiv 7\pmod{25}\}$ or $\{n\equiv 18\pmod{25}\}$. Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_5107ee72f5fc1c30 | Erdős Problem #333 has status 'disproved (lean)'. Topics: number theory, additive basis. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_510ba88d9583e379 | Erdős Problem #154 has status 'proved (lean)'. Topics: sidon sets. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_51655c949532785b | Erdős Problem #925 has been DISPROVED (a counterexample is known). Topics: graph theory, ramsey theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_51710fcf962c034a | Erdős Problem #812 remains OPEN. Topics: graph theory, ramsey theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A059442. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_51d2512f236268a4 | Erdős Problem #74 remains OPEN. Statement: Let $f(n)\to \infty$ possibly very slowly. Is there a graph of infinite chromatic number such that every finite subgraph on $n$ vertices can be made bipartite by deleting at most $f(n)$ edges? Topics: graph theory, chromatic number, cycles. Erdős prize: $500. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_523a610fc3947249 | OBLIGATION (Erdos #307). BANKED: the congruence-barrier construction verified. OPEN: the unconditional bound remains open. | unreviewed | 0.50 | — | — | asserted · 2d |
| vf_527d4c8d42db1bc3 | Erdős Problem #90 has been DISPROVED (a counterexample is known). Statement: Does every set of $n$ distinct points in $\mathbb{R}^2$ contain at most $n^{1+O(\frac{1}{\log\log n})}$ many pairs which are distance $1$ apart? This was [disproved](https://cdn.openai.com/pdf/74c24085-19b0-4534-9c90-465b8e29ad73/unit-distance-proof.pdf) by an internal model at OpenAI, which constructed (for infinitely many $n$) a set $P$ of $n$ points in $\mathbb{R}^2$ such that the number of unit distance pairs in $P$ is at least $n^{1+c}$, where $c > 0$ is an absolute constant. Topics: geometry, distances. Erdős prize: $500. Statement is machine-verified in Lean (formal-conjectures). OEIS: A186705. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_52a87380fe02a383 | Erdős Problem #1088 remains OPEN. Topics: geometry. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_52fb3e220a67b544 | Erdős Problem #240 has been PROVED (Erdős's conjecture holds). Topics: number theory, primes. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_5300268135fc4490 | Erdős Problem #931 remains OPEN. Statement: Let $k_1 \geq k_2 \geq 3$. Are there only finitely many $n_2\geq n_1 + k_1$ such that $$ \prod_{1\leq i\leq k_1}(n_1 + i)\ \text{and}\ \prod_{1\leq j\leq k_2} (n_2 + j) $$ have the same prime factors? Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_5334e736aaa30c6d | Erdős Problem #466 has been PROVED (Erdős's conjecture holds). Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_53be11eedaed1c71 | Erdős Problem #25 remains OPEN. Statement: Let $n_1 < n_2 < \dots$ be an arbitrary sequence of integers, each with an associated residue class $a_i \pmod{n_i}$. Let $A$ be the set of integers $n$ such that for every $i$ either $n < n_i$ or $n \not\equiv a_i \pmod{n_i}$. Must the logarithmic density of $A$ exist? Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_53c48b5730a23688 | Erdős Problem #1041 has status 'falsifiable'. Statement: Let $$ f(z) = \prod_{i=1}^{n} (z - z_i) \in \mathbb{C}[x] $$ with $|z_i| < 1$ for all $i$. Conjecture: Must there always exist a path of length less than 2 in $$ \{ z \in \mathbb{C} \mid |f(z)| < 1 \} $$ which connects two of the roots of $f$? Topics: analysis. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_53e983bd0ab0b6d3 | Erdős Problem #569 remains OPEN. Topics: graph theory, ramsey theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_5414e5338eefc572 | Erdős Problem #783 is SOLVED. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_5429451ff0e30d4d | Erdős Problem #973 remains OPEN. Topics: analysis. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_548d85ccc6d3d37c | Erdős Problem #694 has status 'solved (lean)'. Statement: Let $f_\max(n)$ be the largest $m$ such that $\phi(m) = n$, and $f_\min(n)$ be the smallest such $m$, where $\phi$ is Euler's totient function. Investigate $$ \max_{n\leq x}\frac{f_\max(n)}{f_\min(n)}. $$ GPT-5.5 Pro (prompted by Price) has proved (see also the comments for a summary) that $$ \max_{n\leq x}\frac{f_{\max}(n)}{f_{\min}(n)}=(e^\gamma+o(1))\log\log x. $$ A Lean formalisation of the reduction exists, conditional on Mertens' product theorem and Linnik's theorem; see the [formal proof](https://github.com/Shashi456/erdos-formalizations/blob/main/Erdos/P694/Proof.lean). Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_54c1da26ce121a54 | Erdős Problem #199 has status 'disproved (lean)'. Topics: arithmetic progressions. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_54cc00f219eb288e | Erdős Problem #1028 has status 'solved (lean)'. Topics: graph theory, discrepancy. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_54f286a3bed4a743 | Erdős Problem #225 has been PROVED (Erdős's conjecture holds). Topics: analysis. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_5573828ae777d7e6 | Erdős Problem #1101 remains OPEN. Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_55841c2174acba71 | Erdős Problem #1017 remains OPEN. Topics: graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_55921775986ed4e2 | Erdős Problem #155 remains OPEN. Statement: Is it true that for every $k \geq 1$ we have $$ F(N + k) \leq F(N) + 1 $$ for all sufficiently large $N$? Topics: additive combinatorics, sidon sets. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A143824, A227590, A003022. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_55c754d21f86f835 | Erdős Problem #221 has status 'proved (lean)'. Topics: number theory, additive basis. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_560e7b894c20c2ca | Erdős Problem #789 remains OPEN. Statement: Let $h(n)$ be maximal such that if $A\subseteq \mathbb{Z}$ with $\lvert A\rvert=n$ then there is $B\subseteq A$ with $\lvert B\rvert \geq h(n)$ such that if $a_1+\cdots+a_r=b_1+\cdots+b_s$ with $a_i,b_i\in B$ then $r=s$. Estimate $h(n)$. Topics: additive combinatorics. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_567105f7dbeb5508 | Erdős Problem #310 has been PROVED (Erdős's conjecture holds). Topics: number theory, unit fractions. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_5689767635de0ddb | Erdős Problem #1004 remains OPEN. Statement: For any fixed c > 0, if x is sufficiently large then there exists n ≤ x such that the values of φ(n+k) are all distinct for 1 ≤ k ≤ (log x)^c. This is an open problem. Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_569781b8d736757b | Erdős Problem #378 has been PROVED (Erdős's conjecture holds). Topics: number theory, binomial coefficients. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_569cc28f320a0b1e | Erdős Problem #942 remains OPEN. Statement: Is there some constant $c > 0$ such that $h(n) < (\log n)^{c + o(1)}$ and, for infinitely many $n$, $h(n) > (\log n)^{c - o(1)}$. Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_56d47a192d3fd55c | Erdős Problem #112 remains OPEN. Topics: graph theory, ramsey theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_5700df7254589a75 | Erdős Problem #565 has been PROVED (Erdős's conjecture holds). Topics: graph theory, ramsey theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_571a72065852ca9f | Erdős Problem #778 remains OPEN. Topics: graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_578aedd21b24562b | Erdős Problem #891 remains OPEN. Statement: Let $2=p_1 < p_2 < \cdots$ be the primes and $k\geq 2$. Is it true that, for all sufficiently large $n$, there must exist an integer in $[n,n+p_1\cdots p_k)$ with $>k$ many prime factors? Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_579e87efc5849abd | Erdős Problem #1060 remains OPEN. Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A327153. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_57f9e7996cfba4d4 | Erdős Problem #662 remains OPEN. Topics: geometry, distances. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_58a8057a0e08b98b | Erdős Problem #1078 has been PROVED (Erdős's conjecture holds). Topics: graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_58dca3cb8a12d084 | Erdős Problem #661 remains OPEN. Topics: geometry, distances. Erdős prize: $50. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_59580c605eefc31a | Erdős Problem #737 has been PROVED (Erdős's conjecture holds). Topics: graph theory, chromatic number. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_597b73b7a6195db8 | Erdős Problem #260 remains OPEN. Statement: Let $a_1 < a_2 < \cdots$ be an increasing sequence such that $\frac{a_n}{n} \to \infty$. Is the sum $\sum_{n}^{\infty} \frac{a_n}{2^{a_n}}$ irrational? Topics: irrationality. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_5991d605f324bd7c | Erdős Problem #989 is SOLVED. Topics: discrepancy. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_59a7700427680064 | Erdős Problem #856 remains OPEN. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_59e65c8826f3b40e | Erdős Problem #597 remains OPEN. Topics: graph theory, ramsey theory, set theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_5a09d6d7bf61bf93 | Erdős Problem #491 has been PROVED (Erdős's conjecture holds). Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_5a12936da724c9f1 | Erdős Problem #964 has status 'proved (lean)'. Topics: number theory, divisors. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_5a2c00494580cf86 | Erdős Problem #28 remains OPEN. Statement: If $A ⊆ \mathbb{N}$ is such that $A + A$ contains all but finitely many integers then $\limsup 1_A ∗ 1_A(n) = \infty$. Topics: number theory, additive basis. Erdős prize: $500. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_5a306a8baffd1ea7 | Erdős Problem #405 has been PROVED (Erdős's conjecture holds). Topics: number theory, factorials. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_5a4e70b63d325a9b | Erdős Problem #615 has been DISPROVED (a counterexample is known). Topics: graph theory, ramsey theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_5a65e348c1b296c0 | Erdős Problem #386 remains OPEN. Statement: There is a $k$, such that $2 \le k \le n - 2$ and $\binom{n}{k}$ can be the product of consecutive primes infinitely often? Topics: number theory, binomial coefficients. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A280992. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_5a7a3980e78309c1 | Erdős Problem #838 remains OPEN. Topics: geometry, convex. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_5a942f0058ab7867 | Erdős Problem #78 remains OPEN. Topics: graph theory, ramsey theory. Erdős prize: $100. Not yet formalized in Lean. OEIS: A059442. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_5a9fb0a347253baa | Erdős Problem #853 remains OPEN. Topics: number theory, primes. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A001223, A390769. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_5ac7ef7cbc037ffc | Erdős Problem #927 has been DISPROVED (a counterexample is known). Topics: graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_5acbcb216f92fdc4 | Erdős Problem #1069 is SOLVED. Topics: geometry. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_5acc5e4912d47f8f | Erdős Problem #969 remains OPEN. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: A013928. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_5ae06d9db89402a0 | Erdős Problem #1206 remains OPEN. Topics: number theory, sidon sets. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_5ae70ea1d3361423 | Erdős Problem #429 has status 'disproved (lean)'. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_5af06e4352c07401 | Erdős Problem #1172 remains OPEN. Topics: set theory, ramsey theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_5af54bfa527481ff | Erdős Problem #1199 remains OPEN. Statement: Is it true that in any 2-colouring of $\mathbb{N}$ there exists an infinite set $A$ such that all elements of $A+A$ are the same colour? A conjecture of Owings [Ow74]. Topics: additive combinatorics, ramsey theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_5b097558b6d30b73 | Erdős Problem #401 has status 'proved (lean)'. Topics: number theory, factorials. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_5b241cef7cca337a | Erdős Problem #552 remains OPEN. Topics: graph theory, ramsey theory. Erdős prize: no. Not yet formalized in Lean. OEIS: A006672. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_5be34b3462c35345 | Erdős Problem #793 remains OPEN. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_5c2492c76e5ab29d | Erdős Problem #746 has been PROVED (Erdős's conjecture holds). Topics: graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_5c5b9d441b3e35ef | Erdős Problem #478 remains OPEN. Topics: number theory, factorials. Erdős prize: no. Not yet formalized in Lean. OEIS: A210184. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_5c99806040afefde | Erdős Problem #1121 has status 'proved (lean)'. Topics: geometry. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_5cdf3e8b0dd5bf7a | Erdős Problem #614 remains OPEN. Topics: graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_5d0311805885804a | Erdős Problem #632 has been DISPROVED (a counterexample is known). Topics: graph theory, chromatic number. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_5d81b9c00d26aa68 | Erdős Problem #88 has been PROVED (Erdős's conjecture holds). Topics: graph theory, ramsey theory. Erdős prize: $100. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_5d8ab371ac6fe3c5 | Erdős Problem #1203 remains OPEN. Statement: Prove that $F(n)\to \infty$ as $n\to \infty$. Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_5dda7d31253d867c | Erdős Problem #480 has been PROVED (Erdős's conjecture holds). Statement: Let $x_1,x_2,\ldots\in [0,1]$ be an infinite sequence. Is it true that $$\inf_n \liminf_{m\to \infty} n \lvert x_{m+n}-x_m\rvert\leq 5^{-1/2}\approx 0.447?$$ A conjecture of Newman. Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_5dfd5a994314c632 | Erdős Problem #624 remains OPEN. Statement: Let $X$ be a finite set of size $n$ and $H(n)$ be such that there is a function $f:\{A : A\subseteq X\}\to X$ so that for every $Y\subseteq X$ with $\lvert Y\rvert \geq H(n)$ we have $\left\{ f(A) : A\subseteq Y\right\}=X$. Prove that $H(n)-\log_2 n \to \infty$. Topics: combinatorics. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_5e2c4a7007323880 | Erdős Problem #894 has been PROVED (Erdős's conjecture holds). Topics: number theory, ramsey theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_5e54241096a63cb2 | Erdős Problem #996 remains OPEN. Statement: Does there exists a positive constant `C` such that for all `f ∈ L²[0,1]` and all lacunary sequences `n`, if `‖f - fₖ‖₂ = O(1 / log log log k ^ C)`, then for almost every `x`, `lim ∑ k ∈ Finset.range N, f (n k • x)) / N = ∫ t, f t ∂t`? Topics: analysis. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_5ef61a96cfccef5d | Erdős Problem #278 remains OPEN. Topics: number theory, covering systems. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_5f64d8060fa9a4a1 | Erdős Problem #355 has status 'proved (lean)'. Statement: Is there a lacunary sequence $A\subseteq \mathbb{N}$ (so that $A=\{a_1 < \cdots\}$ and there exists some $\lambda > 1$ such that $a_{n+1}/a_n\geq \lambda$ for all $n\geq 1$) such that $$\left\{ \sum_{a\in A'}\frac{1}{a} : A'\subseteq A\textrm{ finite}\right\}$$ contain all rationals in some open interval? Bleicher and Erdős conjectured the answer is no. In fact the answer is yes, with any lacunarity constant $\lambda\in (1,2)$ (though not $\lambda=2$), as proved by van Doorn and Kova\v{c} [DoKo25]. This was formalized in Lean by van Doorn using Aristotle. Topics: number theory, unit fractions. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_5f64fd5b2e6f5e30 | Erdős Problem #1123 has status 'independent'. Topics: algebra. Erdős prize: $100. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_5f91b9804d33b469 | Erdos minimum-overlap problem (1955, partial bounds known): given a partition of {1,...,2n} into A and B with |A|=|B|=n, the minimum over all partitions of max_k |{(a,b) in A x B : b - a = k}| is between c1*n and c2*n with the constants improved iteratively. | unreviewed | 0.60 | — | — | asserted · 13d |
| vf_5fb51737c80b6cca | Erdős Problem #934 remains OPEN. Topics: graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_5fb62155575c5840 | Erdős Problem #36 remains OPEN. Statement: Find the value of the limit of `MinOverlapQuotient`! Topics: number theory, additive combinatorics. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A393584, possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_5fb88a6ce8b40b57 | Erdős Problem #904 has status 'proved (lean)'. Topics: graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_60496604dd5cca5a | Erdős Problem #341 remains OPEN. Statement: Let $A=\{a_1 < \cdots < a_k\}$ be a finite set of integers and extend it to an infinite sequence $\overline{A}=\{a_1 < a_2 < \cdots \}$ by defining $a_{n+1}$ for $n \geq k$ to be the least integer exceeding $a_n$ which is not of the form $a_i + a_j$ with $i,j \leq n$. Is it true that the sequence of differences $a_{m+1}-a_m$ is eventually periodic? This problem is discussed under Problem 7 on Green's open problems list. Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_608ebe818e8a4906 | Erdős Problem #258 has status 'proved (lean)'. Statement: Let $a_n \to \infty$ be a sequence of non-zero natural numbers. Is $\sum_n \frac{d(n)}{(a_1 ... a_n)}$ irrational, where $d(n)$ is the number of divisors of $n$? This was proved affirmatively by Chojecki and GPT-5.4 Pro [Ch26], and formalised in Lean by ster-oc [St26]. Topics: irrationality. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_60a2b72edf78e6c9 | Erdős Problem #33 remains OPEN. Statement: Let `A ⊆ ℕ` be a set such that every integer can be written as `n^2 + a` for some `a` in `A` and `n ≥ 0`. What is the smallest possible value of `lim sup n → ∞ |A ∩ {1, …, N}| / N^(1/2)`? Topics: number theory, additive basis. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_60be642b36c53fcd | Erdős Problem #913 remains OPEN. Statement: Are there infinitely many $n$ such that if $$ n(n + 1) = \prod_i p_i^{k_i} $$ is the factorisation into distinct primes then all exponents $k_i$ are distinct? Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A359747. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_6110c0dcb5f7ca71 | Erdős Problem #1114 has been PROVED (Erdős's conjecture holds). Topics: analysis, polynomials. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_612ae3dc6d8bf729 | Erdős Problem #712 remains OPEN. Topics: graph theory, turan number, hypergraphs. Erdős prize: $500. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_614a136a5e3f56d2 | Erdős Problem #741 has status 'solved (lean)'. Topics: additive combinatorics. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_61c6a46c0bd5227e | Erdős Problem #195 remains OPEN. Statement: What is the largest $k$ such that in any permutation of $\mathbb{Z}$ there must exist a monotone $k$-term arithmetic progression $x_1 < \cdots < x_k$? Topics: arithmetic progressions. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_623a3e249fa2fe2d | Erdős Problem #532 has status 'proved (lean)'. Topics: number theory, ramsey theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_62546627839c96be | Erdős Problem #274 remains OPEN. Statement: Does there exist a group `G` with an exact covering by more than one cosets of different sizes? (i.e. each element is contained in exactly one of the cosets.) Topics: group theory, covering systems. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_625e59d23a049af7 | Erdős Problem #217 remains OPEN. Topics: geometry, distances. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_627bc4417db3f419 | Erdős Problem #482 is SOLVED. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: A004539. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_6294373d9e52c01a | Erdős Problem #854 remains OPEN. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: A389839, A048670. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_62a45cb98acd1c8d | Erdős Problem #350 has status 'proved (lean)'. Statement: If `A ⊂ ℕ` is a finite set of integers all of whose subset sums are distinct then `∑ n ∈ A, 1/n < 2`. Proved by Ryavec. This was proved by Ryavec, who did not appear to ever publish the proof. Ryavec's proof is reproduced in [BeEr74]. More generally, Ryavec's proof delivers that $\sum_{n\in A}\frac{1}{n}\leq 2-2^{1-\lvert A\rvert},$ with equality if and only if $A=\{1,2,\ldots,2^k\}$. This was formalized in Lean by Alexeev using Aristotle. Topics: number theory, additive combinatorics. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_62e1c97f24fdb9e4 | Erdős Problem #534 is SOLVED. Topics: number theory, intersecting family. Erdős prize: no. Not yet formalized in Lean. OEIS: A387543, A387698. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_631c5e14bdf29505 | Erdős Problem #677 remains OPEN. Statement: Denote by $M(n, k)$ the least common multiple of the finite set $\{n+1, \dotsc, n+k\}$. Is it true that for all $m \geq n + k$, we get $M(m, k) \neq M(n, k)$? Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_638ddfe7e397586b | Erdős Problem #336 remains OPEN. Topics: number theory, additive basis. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_63af231e25f6c231 | Erdős Problem #424 remains OPEN. Statement: Let $a_1 = 2$ and $a_2 = 3$ and continue the sequence by appending to $a_1, \ldots, a_n$ all possible values of $a_i a_j - 1$ with $i \neq j$. Is it true that the set of integers which eventually appear has positive density? Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A005244. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_63bacba0f420c7ca | Erdős Problem #507 remains OPEN. Topics: geometry. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_63cf7f09150f3200 | Erdős Problem #125: machine-found Lean proof published by AlphaProof Nexus (DeepMind, arXiv 2605.22763, May 2026) (positive-lower-density variant — the formalized statement is a variant, not necessarily the full original problem). Independently re-verified locally 2026-06-10: full lake build of google-deepmind/alphaproof-nexus-results@0647711a7118 under their pinned toolchain leanprover/lean4:v4.27.0 succeeded (8062 jobs); static scan clean (no sorry, no native_decide, no custom axioms). Artifacts: erdos_125.variants.positive_lower_density.lean sha256:12e2df1ba973bde5. AI involvement: machine-generated proof, machine-checked (Lean kernel is the referee); statement faithfulness NOT yet independently attested — see paper section 4 for DeepMind's own expert validation. | unreviewed | 0.90 | — | — | attested · 2d |
| vf_63d77f7d21921993 | Erdős Problem #673 has been PROVED (Erdős's conjecture holds). Topics: number theory, divisors. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_6473c73966975699 | Erdős Problem #1012 is SOLVED. Topics: graph theory. Erdős prize: no. Not yet formalized in Lean. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_64c18e8bcb349c92 | Erdős Problem #745 has been PROVED (Erdős's conjecture holds). Topics: graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_64f9035e830dd3c9 | Erdős Problem #481 has status 'proved (lean)'. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_650fe85c73773446 | Erdős Problem #1000 has status 'proved (lean)'. Topics: number theory, diophantine approximation. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_6514a3669c0d3857 | Erdős Problem #396 remains OPEN. Statement: Is it true that for every $k$ there exists $n$ such that $$\prod_{0\leq i\leq k}(n-i) \mid \binom{2n}{n}?$$ Topics: number theory, binomial coefficients. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A375077. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_6538f0d0e4d5366a | Erdős Problem #1122 remains OPEN. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_65443aa22fb48998 | Erdős Problem #77 remains OPEN. Topics: graph theory, ramsey theory. Erdős prize: $250. Not yet formalized in Lean. OEIS: A059442. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_655f6d08a3c838dd | Erdős Problem #874 has been PROVED (Erdős's conjecture holds). Topics: number theory, additive combinatorics. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_6564bbed5be3849b | Erdős Problem #1053 remains OPEN. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: A007539. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_656c20b90898152d | Erdős Problem #744 has been DISPROVED (a counterexample is known). Topics: graph theory, chromatic number. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_656c5f65f942572a | Erdős Problem #506 has status 'decidable'. Topics: geometry. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_657104d54d25d9ba | Erdős Problem #467 remains OPEN. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_6596a7dd831c7b16 | Erdős Problem #471 has been PROVED (Erdős's conjecture holds). Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_659a28db5759e165 | Erdős Problem #185 has been PROVED (Erdős's conjecture holds). Topics: additive combinatorics. Erdős prize: no. Not yet formalized in Lean. OEIS: A003142. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_65e23e86a33c7f64 | Erdős Problem #455 remains OPEN. Statement: Let `q : ℕ → ℕ` be a strictly increasing sequence of primes such that `q (n + 2) - q (n + 1) ≥ q (n + 1) - q n`. Must `lim q n / (n ^ 2) = ∞`? Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_6606b97e12b7a882 | Erdős Problem #207 has been PROVED (Erdős's conjecture holds). Topics: combinatorics, hypergraphs. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_662f8a35d217c7b0 | Erdős Problem #254 remains OPEN. Statement: Let $A\subseteq \mathbb{N}$ be such that $\lvert A\cap [1,2x]\rvert -\lvert A\cap [1,x]\rvert \to \infty\textrm{ as }x\to \infty$ and $\sum_{n\in A} \{ \theta n\}=\infty$ for every $\theta\in (0,1)$, where $\{x\}$ is the distance of $x$ from the nearest integer. Then every sufficiently large integer is the sum of distinct elements of $A$. Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_663ef26e7045ee26 | Erdős Problem #340 remains OPEN. Statement: Let $A = \{1, 2, 4, 8, 13, 21, 31, 45, 66, 81, 97, \ldots\}$ be the greedy Sidon sequence: we begin with $1$ and iteratively include the next smallest integer that preserves the Sidon property (i.e. there are no non-trivial solutions to $a + b = c + d$). What is the order of growth of $A$? Is it true that $|A \cap \{1, \ldots, N\}| \gg N^{1/2 - \varepsilon}$ for all $\varepsilon > 0$ and large $N$? Topics: number theory, additive combinatorics, sidon sets. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A080200, A005282. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_6688760ece116e05 | Erdős Problem #1035 remains OPEN. Topics: graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_66f237af53015435 | Erdős Problem #140 has been PROVED (Erdős's conjecture holds). Topics: additive combinatorics, arithmetic progressions. Erdős prize: $500. Not yet formalized in Lean. OEIS: A003002. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_66ff04a041674bcf | Erdős Problem #233 remains OPEN. Statement: A conjecture by Heath-Brown: The sum of squares of the first $N$ gaps between consecutive primes behaves like $N * (log N)^2$. Topics: number theory, primes. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A074741. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_67186eac9081b664 | Erdős Problem #983 remains OPEN. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_6761c546b5fdeac8 | Erdős Problem #477 remains OPEN. Statement: Is there a polynomial $f:\mathbb{Z}\to \mathbb{Z}$ of degree at least $2$ and a set $A\subset \mathbb{Z}$ such that for any $z\in \mathbb{Z}$ there is exactly one $a\in A$ and $b\in \{ f(n) : n\in\mathbb{Z}\}$ such that $z=a+b$? Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_676270d3358f7d9b | Erdős Problem #365 remains OPEN. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: A060355, A060859, A175155. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_6777433d91a2fad5 | Erdős Problem #916 has been PROVED (Erdős's conjecture holds). Topics: graph theory, cycles. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_677854c3a46c4e49 | Erdős Problem #638 remains OPEN. Topics: graph theory, ramsey theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_677acb2a78fb7dc3 | Erdős Problem #583 has status 'falsifiable'. Topics: graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_678a8b5ebe1873b2 | Erdős Problem #779 has status 'falsifiable'. Statement: A Conjecture of Marian Deaconescu, see p.120 in https://doi.org/10.2307/2975810 [Needed to index shift in order to avoid trivial case $n = 0$, where the conjecture is trivially false.] Topics: number theory, primes. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A005235. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_679c45b68e39bd9f | Erdős Problem #833 has been PROVED (Erdős's conjecture holds). Topics: graph theory, hypergraphs, chromatic number. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_67ede92ae28364ac | Erdős Problem #872 remains OPEN. Topics: number theory, primitive sets. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_680fb5be53ac0fb1 | Erdős Problem #1170 remains OPEN. Topics: set theory, ramsey theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_68774d93c875b4da | Erdős Problem #318 is SOLVED. Topics: number theory, unit fractions. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_6893403e9e6123d1 | Erdős Problem #824 remains OPEN. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_68c1a3797e659b41 | Erdős Problem #468 remains OPEN. Topics: number theory, divisors. Erdős prize: no. Not yet formalized in Lean. OEIS: A167485, A387502, A387503. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_68da9c7502a44d9f | Erdős Problem #935 remains OPEN. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: A057521, A389244, possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_68df117a797f45cf | Erdős Problem #317 remains OPEN. Statement: Is there some constant $c>0$ such that for every $n\geq 1$ there exists some $\delta_k\in \{-1,0,1\}$ for $1\leq k\leq n$ with $$0< \left\lvert \sum_{1\leq k\leq n}\frac{\delta_k}{k}\right\rvert < \frac{c}{2^n}?$$ Topics: number theory, unit fractions. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_690c098f78207d2a | Erdős Problem #651 has been DISPROVED (a counterexample is known). Topics: geometry, convex. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_6913509c74f825b8 | Erdős Problem #406 remains OPEN. Statement: Is it true that there are only finitely many powers of $2$ which have only the digits $0$ and $1$ when written in base $3$? Topics: number theory, base representations. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_6914e31e9688153b | Erdős Problem #145 remains OPEN. Statement: Let $s_1 < s_2 < \cdots$ be the sequence of squarefree numbers. Is it true that, for any $\alpha\geq 0$, $$ \lim_{x\to\infty} \frac{1}{x}\sum_{s_n\leq x}(s_{n+1}-s_n)^\alpha $$ exists? Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A005117. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_692d5636776bad32 | Erdős Problem #334 remains OPEN. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: A062241, A045535. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_69879ad2179469cd | Erdős Problem #1149 has been PROVED (Erdős's conjecture holds). Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_69bbc811795793c3 | Erdős Problem #995 remains OPEN. Topics: analysis, discrepancy. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_69c06e3a0b72560d | Erdős Problem #963 remains OPEN. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_69f69f3a459f7423 | Erdős Problem #408 remains OPEN. Topics: number theory, iterated functions. Erdős prize: no. Not yet formalized in Lean. OEIS: A049108. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_6a279e3146de8c75 | Erdős Problem #527 has been PROVED (Erdős's conjecture holds). Topics: analysis, probability. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_6a75a7dc515281fe | Erdős Problem #1007 has status 'solved (lean)'. Topics: graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_6a8399c8cd82fbe9 | Erdős Problem #1023 has status 'solved (lean)'. Topics: combinatorics. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_6a94941948263af4 | Erdős Problem #665 remains OPEN. Topics: combinatorics. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_6ab0d203c3662492 | Erdős Problem #47 has status 'proved (lean)'. Topics: number theory, unit fractions. Erdős prize: $100. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_6ac7397300551f95 | Erdős Problem #183 remains OPEN. Topics: graph theory, ramsey theory. Erdős prize: $250. Not yet formalized in Lean. OEIS: A003323. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_6acf5cc449d953d5 | Erdős Problem #941 has been PROVED (Erdős's conjecture holds). Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: A056828. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_6b3507ac3562beb0 | Erdős Problem #173 remains OPEN. Topics: geometry, ramsey theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_6b49cc29c0091bff | Erdős Problem #980 has been PROVED (Erdős's conjecture holds). Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: A053760, A098990, possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_6b4ba8010dbbad76 | Erdős Problem #91 remains OPEN. Statement: Suppose $A\subset \mathbb{R}^2$ has $\lvert A\rvert=n$ and minimises the number of distinct distances between points in $A$. Prove that for large $n$ there are at least two (and probably many) such $A$ which are non-similar. Topics: geometry, distances. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A186704, possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_6babf4f5c4c906fd | Erdős Problem #1010 has been PROVED (Erdős's conjecture holds). Topics: graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_6bba655c592a2074 | Erdős Problem #182 has been PROVED (Erdős's conjecture holds). Topics: graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_6bf3b133b2018523 | Erdős Problem #701 remains OPEN. Statement: Let $\mathcal{F}$ be a family of sets closed under taking subsets (i.e. if $B\subseteq A\in\mathcal{F}$ then $B\in \mathcal{F}$). There exists some element $x$ such that whenever $\mathcal{F}'\subseteq \mathcal{F}$ is an intersecting subfamily we have $$\lvert \mathcal{F}'\rvert \leq \lvert \{ A\in \mathcal{F} : x\in A\}\rvert.$$ Topics: combinatorics, intersecting family. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_6d13d53b8f7657df | Erdős Problem #1193 has status 'solved (lean)'. Topics: additive combinatorics. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_6daee84810e2037d | Erdős Problem #1168 remains OPEN. Topics: set theory, ramsey theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_6ddad4144c43d0b4 | Erdős Problem #509 remains OPEN. Statement: Let $f(z) ∈ ℂ[z]$ be a monic non-constant polynomial. Can the set $\{z ∈ ℂ : |f(z)| ≤ 1\}$ be covered by a set of closed discs the sum of whose radii is $≤ 2$? Topics: analysis. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_6e126f3f5046840d | Erdős Problem #7 has status 'verifiable'. Statement: Is there a covering system all of whose moduli are odd (and greater than 1)? Topics: number theory, covering systems. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_6e39ebc5057975d7 | Erdős Problem #822 has been PROVED (Erdős's conjecture holds). Statement: Does the set of integers of the form $n + \varphi(n)$ have positive (lower) density? [GIL24] proved this was true. Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A121048, A155085. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_6e7e538b3a9d15d1 | Erdős Problem #579 remains OPEN. Topics: graph theory, turan number. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_6ea4019ad9017c9b | Erdős Problem #1113 remains OPEN. Statement: **Erdős Problem 1113.** Do there exist Sierpiński numbers that possess no finite covering set of primes? Erdős and Graham [ErGr80] conjectured that the answer is yes. A negative answer would imply that there are infinitely many Fermat primes. Topics: number theory, covering systems. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A076336. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_6f2cd092f1ae24b5 | Erdős Problem #880 has been PROVED (Erdős's conjecture holds). Topics: number theory, additive basis. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_6f307ef73915ae96 | Erdős Problem #3 remains OPEN. Statement: If $A \subset \mathbb{N} has $\sum_{n \in A}\frac 1 n = \infty$, then must $A$ contain arbitrarily long arithmetic progressions? Topics: number theory, additive combinatorics, arithmetic progressions. Erdős prize: $5000. Statement is machine-verified in Lean (formal-conjectures). OEIS: A003002, A003003, A003004, A003005. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_6f3da9ac8942c79d | Erdős Problem #977 has been PROVED (Erdős's conjecture holds). Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: A005420, A002583. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_6f72991dca061b6b | Erdős Problem #766 remains OPEN. Topics: graph theory, turan number. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_6f7a2ba131b30100 | Erdős Problem #591 has been PROVED (Erdős's conjecture holds). Statement: Let $α$ be the infinite ordinal $\omega^{\omega^2}$. Is it true that any red/blue colouring of the edges of $K_α$ there is either a red $K_α$ or a blue $K_3$? This is true and was proved independently by Schipperus [Sc10] and Darby. Topics: set theory, ramsey theory. Erdős prize: $250. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_6fb4c79feee524ac | Erdős Problem #1147 has been DISPROVED (a counterexample is known). Topics: irrational, additive basis. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_6fca339d3d65e90b | Erdős Problem #832 has been DISPROVED (a counterexample is known). Topics: graph theory, hypergraphs, chromatic number. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_6fd2e4c31e5b09bc | Erdős Problem #817 remains OPEN. Statement: Let $k \geq 3$. Define $g_k(n)$ to be the minimal $N$ such that $\{1, ..., N\}$ contains some $A$ of size $|A| = n$ such that $$ \langle A\rangle = \left\{\sum_{a \in A} \epsilon_a a : \epsilon_a \in\{0, 1\}\right\} $$ contains no non-trivial $k$-term arithmetic progression. Estimate $g_k(n)$. In particular, is it true that $$ g_3(n) \gg 3^n $$ Topics: additive combinatorics. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_6feea96dc40c38ff | Erdős Problem #144 has been PROVED (Erdős's conjecture holds). Topics: number theory, divisors. Erdős prize: $250. Not yet formalized in Lean. OEIS: A005279. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_701de0b445e51a9c | Erdős Problem #756 has status 'proved (lean)'. Topics: geometry, distances. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_7056fb210618658b | Erdős Problem #906 remains OPEN. Statement: Does there exists an entire non-zero transcendental function `f : ℂ → ℂ` such that for any sequence `n₀ < n₁ < ...`, `{ z | ∃ k, iteratedDeriv (n k) f z = 0 }` is dense. Topics: analysis, iterated functions. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_705ba873da4c184e | Erdős Problem #417 remains OPEN. Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A264810, A061070. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_7062a5bce7d91dc2 | Erdős Problem #1054 remains OPEN. Topics: number theory, divisors. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A167485. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_706399dc1296a4a5 | Erdős Problem #1074 remains OPEN. Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A063980, A064164. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_7092ab18d9228fe7 | Erdős Problem #1169 has status 'not disprovable'. Topics: set theory, ramsey theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_709c4a90e3d0f898 | Erdős Problem #215 has been PROVED (Erdős's conjecture holds). Topics: geometry. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_70a584f49122d4d4 | Erdős Problem #114 has status 'falsifiable'. Topics: polynomials, analysis. Erdős prize: $250. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_70eb839910df9449 | Erdős Problem #266 has been DISPROVED (a counterexample is known). Statement: Let $a_n$ be an infinite sequence of positive integers such that $\sum \frac{1}{a_n}$ converges. There exists some integer $t \ge 1$ such that $\sum \frac{1}{a_n + t}$ is irrational. This was disproven by Kovač and Tao in [KoTa24]. [KoTa24] Kovač, V. and Tao T., On several irrationality problems for Ahmes series. [arXiv:2406.17593](https://arxiv.org/abs/2406.17593) (2024). Topics: irrationality. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_70f11d3a5426c0fc | Erdős Problem #690 is SOLVED. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_70fe5e818f885d1f | Erdős Problem #908 has been PROVED (Erdős's conjecture holds). Topics: analysis. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_71b60161e7c5f1a4 | Erdős Problem #375 has status 'falsifiable'. Statement: Is `Erdos375Prop` true? Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_71f6b087d1a8777c | Erdős Problem #855 remains OPEN. Statement: Erdős Problem 855 (Segal's conjecture): $\pi(x + y) \le \pi(x) + \pi(y)$ for sufficiently large $x, y$. Topics: number theory, primes. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A023193. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_7218fd69b508900f | Erdős Problem #1155 remains OPEN. Topics: graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_7258cefad7519006 | Erdős Problem #316 has status 'disproved (lean)'. Statement: Is it true that if $A \subseteq \mathbb{N}\setminus\{1\}$ is a finite set with $\sum_{n \in A} \frac{1}{n} < 2$ then there is a partition $A=A_1 \sqcup A_2$ such that $\sum_{n \in A_i} \frac{1}{n} < 1$ for $i=1,2$? This is not true in general, as shown by Sándor [Sa97]. The minimal counterexample is $\{2,3,4,5,6,7,10,11,13,14,15\}$, found by Tom Stobart. This was formalized in Lean by Mehta. Topics: number theory, unit fractions. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_732209afe049543e | Erdős Problem #465 has been PROVED (Erdős's conjecture holds). Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_7333b399cfc64473 | Erdős Problem #187 remains OPEN. Topics: additive combinatorics, ramsey theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_734dc958835d0249 | Erdős Problem #414 remains OPEN. Statement: Let $h_1(n) = h(n)$ and $h_k(n) = h(h_{k-1}(n))$. Is it true, for any $m,n$, there exist $i$ and $j$ such that $h_i(m) = h_j(n)$? Topics: number theory, iterated functions. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A064491, possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_7372f85768f7857c | Erdős Problem #1136 has status 'proved (lean)'. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_7373179525dda5d9 | Erdős Problem #1096 has been PROVED (Erdős's conjecture holds). Statement: Let $1<q<1+\epsilon$ and consider the set of numbers of the shape $\sum_{i\in S}q^i$ (for all finite $S$), ordered by size as $0=x_1<x_2<\cdots$. Is it true that, provided $\epsilon>0$ is sufficiently small, $x_{k+1}-x_k \to 0$? This was solved affirmatively by Erdős and Komornik [ErKo98], who proved the conclusion whenever $1<q<\sqrt{q_1}$, where $q_1$ is the second Pisot-Vijayaraghavan number. Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_73786d32aad4f6c7 | Erdős Problem #936 remains OPEN. Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A146968, possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_737f7b675768b136 | Erdős Problem #733 has been PROVED (Erdős's conjecture holds). Topics: combinatorics, geometry. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_73a27d55bb758f68 | Erdős Problem #372 has been PROVED (Erdős's conjecture holds). Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: A071870. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_73cd34a5624f795b | Erdős Problem #394 remains OPEN. Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A344005. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_73df0395b73a7c38 | Erdős Problem #754 has been PROVED (Erdős's conjecture holds). Topics: geometry, distances. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_73f59090daaf10b5 | Erdős Problem #119 remains OPEN. Topics: analysis, polynomials. Erdős prize: $100. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_744150b90ccf3833 | Erdős Problem #649 has status 'disproved (lean)'. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_74448d988565c839 | Erdős Problem #1097 remains OPEN. Statement: The main conjecture: for any finite set of integers $A$ with $|A| = n$, the number of distinct common differences in three-term arithmetic progressions is $O(n^{3/2})$. This conjecture was resolved negatively by showing that the problem is exactly equivalent to Bourgain's sums-differences question [Bo99], which was introduced as an arithmetic path towards the Kakeya conjecture. Under this equivalence: - The greatest achievable exponent for this problem is equal to the smallest constant $c$ achievable for Bourgain's sums-differences question: $$|A -_G B| \ll \max(|A|, |B|, |A +_G B|)^c$$ - The $O(n^{3/2})$ prediction is disproved because the lower bound has been shown to satisfy $c \ge 1.77898$ (due to Zheng and AlphaEvolve [GGTW25], improving on Lemm [Le15]), which is strictly greater than $3/2 = 1.5$. - The best known upper bound is $c \le 11/6 \approx 1.833$ (due to Katz and Tao [KaTa99]). - While the specific $O(n^{3/2})$ prediction is resolved negatively, the general question of determining the exact optimal exponent $c$ remains open. Topics: number theory, additive combinatorics. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_7459e8ca13d2be43 | Erdős Problem #582 has status 'proved (lean)'. Topics: graph theory, ramsey theory. Erdős prize: $100. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_74613932d98ed2c7 | Erdős Problem #227 has been DISPROVED (a counterexample is known). Topics: analysis. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_748cf8097c3816cf | Erdős Problem #741: machine-found Lean proof published by AlphaProof Nexus (DeepMind, arXiv 2605.22763, May 2026). Independently re-verified locally 2026-06-10: full lake build of google-deepmind/alphaproof-nexus-results@0647711a7118 under their pinned toolchain leanprover/lean4:v4.27.0 succeeded (8062 jobs); static scan clean (no sorry, no native_decide, no custom axioms). Artifacts: erdos_741.parts.i.lean sha256:481e87ebaa4058e5; erdos_741.parts.ii.lean sha256:77a222124ab3d8b8. AI involvement: machine-generated proof, machine-checked (Lean kernel is the referee); statement faithfulness NOT yet independently attested — see paper section 4 for DeepMind's own expert validation. | unreviewed | 0.90 | — | — | attested · 2d |
| vf_749c71f85f9c8130 | Erdős Problem #113 has been DISPROVED (a counterexample is known). Topics: graph theory, turan number. Erdős prize: $500. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_757875104f1fb0d7 | Erdős Problem #546 has been PROVED (Erdős's conjecture holds). Topics: graph theory, ramsey theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_757c7eeda08b3450 | Erdős Problem #618 has status 'proved (lean)'. Topics: graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_75fc48b6de0c3749 | Erdős Problem #1212 remains OPEN. Topics: number theory, primes. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_763a75ca856ceea4 | Erdős Problem #81 remains OPEN. Topics: graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_768b7386c895b147 | Erdős Problem #769 remains OPEN. Topics: number theory, geometry. Erdős prize: no. Not yet formalized in Lean. OEIS: A014544, possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_76c4b9427ccea78d | Erdős Problem #1217 has been PROVED (Erdős's conjecture holds). Topics: number theory, divisors, primitive sets. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_77104965cae9b402 | Erdős Problem #1175 remains OPEN. Statement: Let $\kappa$ be an uncountable cardinal. Must there exist a cardinal $\lambda$ such that every graph with chromatic number $\lambda$ contains a triangle-free subgraph with chromatic number $\kappa$? Shelah proved that a negative answer is consistent when $\kappa = \lambda = \aleph_1$ (see `erdos_1175.variants.shelah_consistency`). Topics: set theory, chromatic number. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_7720f17ed267e6ca | Erdős Problem #702 has been PROVED (Erdős's conjecture holds). Topics: combinatorics. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_77394bb921ea67e9 | Erdős Problem #886 remains OPEN. Statement: Let $\epsilon>0$. Is it true that, for all large $n$, the number of divisors of $n$ in $(n^{1/2},n^{1/2}+n^{1/2-\epsilon})$ is $O_\epsilon(1)$? Erdős attributes this conjecture to Ruzsa. Topics: number theory, divisors. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_777ae12ec13f19d5 | Erdős Problem #625 remains OPEN. Topics: graph theory, chromatic number. Erdős prize: $1000. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_77bf228887a3fd3f | Erdős Problem #504 is SOLVED. Topics: geometry. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_77c44d764923687d | Erdős Problem #476 has status 'proved (lean)'. Topics: number theory, additive combinatorics. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_77dc9f28ec1a526b | Erdős Problem #441 has been DISPROVED (a counterexample is known). Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: A068509. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_78181fbe313966eb | Erdős Problem #1196 has status 'proved (lean)'. Statement: Is it true that, for any $x$, if $A\subset [x,\infty)$ is a primitive set of integers (so that no distinct elements of $A$ divide each other) then$$\sum_{a\in A}\frac{1}{a\log a}< 1+o(1),$$where the $o(1)$ term $\to 0$ as $x\to \infty$? - Topics: number theory, primitive sets. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_783a128f9d8b7c87 | Erdős Problem #286 has been PROVED (Erdős's conjecture holds). Topics: number theory, unit fractions. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_7848108680264487 | Erdős Problem #960 has been DISPROVED (a counterexample is known). Topics: geometry. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_7849fc5982c289d2 | Erdős Problem #283 has status 'proved (lean)'. Statement: Let $p\colon \mathbb{Z} \rightarrow \mathbb{Z}$ be a polynomial whose leading coefficient is positive and such that there exists no $d≥2$ with $d ∣ p(n)$ for all $n≥1$. Is it true that, for all sufficiently large $m$, there exist integers $1≤n_1<\dots < n_k$ such that $$1=\frac{1}{n_1}+\cdots+\frac{1}{n_k}$$ and $$m=p(n_1)+\cdots+p(n_k)$$? Topics: number theory, unit fractions. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A380791. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_7865ae2d75a2075b | Erdős Problem #937 has been PROVED (Erdős's conjecture holds). Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_78668daf1aaa1702 | Erdős Problem #525 has been PROVED (Erdős's conjecture holds). Topics: analysis, probability, polynomials. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_79066cec6597486d | Erdős Problem #918 remains OPEN. Topics: graph theory, chromatic number. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_790d21026f417b5d | Erdős Problem #444 has been PROVED (Erdős's conjecture holds). Topics: number theory, divisors. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_790fcc99a314fb3c | Erdős Problem #750 remains OPEN. Statement: Let $f(m)$ be some function such that $f(m)\to \infty$ as $m\to \infty$. Does there exist a graph $G$ of infinite chromatic number such that every subgraph on $m$ vertices contains an independent set of size at least $\frac{m}{2}-f(m)$? Note that in [Er94b] the function $f$ generalises a (proven) result for $f(m) = \epsilon m$, where $\epsilon > 0$. Hence we should assume it is non-negative valued. Topics: graph theory, chromatic number. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_791f20830981267e | Erdős Problem #636 has been PROVED (Erdős's conjecture holds). Topics: graph theory, ramsey theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_796dbf50dd96894d | Erdős Problem #167 has status 'falsifiable'. Topics: graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_797aeeb79bc116d2 | Erdős Problem #805 remains OPEN. Topics: graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_7a226f29da63b3f3 | Erdős Problem #203 remains OPEN. Statement: Is there an integer $m$ with $(m, 6) = 1$ such that none of $2^k \cdot 3^\ell \cdot m + 1$ are prime, for any $k, \ell \ge 0$? Topics: primes, covering systems. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_7a5088c28448c2c9 | Erdős Problem #288 remains OPEN. Statement: Is it true that there are only finitely many pairs of intervals $I_1$, $I_2$ such that $$ \sum_{n_1 \in I_1} \frac{1}{n_1} + \sum_{n_2 \in I_2} \frac{1}{n_2} \in \mathbb{N}? $$ Topics: number theory, unit fractions. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_7a6047639e51c225 | Erdős Problem #787 remains OPEN. Topics: additive combinatorics. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_7a91f60933122865 | Erdős Problem #351 has status 'proved (lean)'. Statement: Let $p(x) \in \mathbb{Q}[x]$ be a non-constant rational polynomial with positive leading coefficient. Is it true that $$A=\{ p(n)+1/n : n \in \mathbb{N}\}$$ is strongly complete, in the sense that, for any finite set $B$, $$\left\{\sum_{a \in X} a : X \subseteq A \setminus B, X \textrm{ is finite}\right\}$$ contains all sufficiently large integers? Topics: number theory, complete sequences. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_7a978d020c61fb24 | Erdős Problem #726 remains OPEN. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_7b03cbeb315f6f44 | Erdős Problem #486 remains OPEN. Statement: For each $n \in \mathbb{N}$ choose some $X_n \subseteq \mathbb{Z}/n\mathbb{Z}$. Let $B = \{m \in \mathbb{N} : \forall n, m \not\equiv x \pmod{n} \text{ for all } x \in X_n\}$. Must $B$ have a logarithmic density? Topics: number theory, primitive sets. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_7b4f03a3ab243292 | Erdős Problem #922 has been PROVED (Erdős's conjecture holds). Topics: graph theory, chromatic number. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_7b739ee86aa8c9e6 | Erdős Problem #613 has status 'disproved (lean)'. Statement: **Erdős Problem 613:** Let $n \geq 3$ and $G$ be a graph with $\binom{2n+1}{2} - \binom{n}{2} - 1$ edges. Must $G$ be the union of a bipartite graph and a graph with maximum degree less than $n$? Topics: graph theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_7c34e714a77b303f | Erdős Problem #411 remains OPEN. Topics: number theory, iterated functions. Erdős prize: no. Not yet formalized in Lean. OEIS: A383044, possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_7c3af07dbda5e463 | Erdős Problem #1134 has been DISPROVED (a counterexample is known). Topics: number theory. Erdős prize: £10. Not yet formalized in Lean. OEIS: A185661. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_7c5a3efc038bdd1c | Erdős Problem #1092 has been DISPROVED (a counterexample is known). Topics: geometry, chromatic number. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_7c8e36025392603f | Erdős Problem #56 has status 'disproved (lean)'. Statement: Suppose $A \subseteq \{1,\dots,N\}$ is such that there are no $k+1$ elements of $A$ which are relatively prime. An example is the set of all multiples of the first $k$ primes. Is this the largest such set? To avoid trivial counterexamples, we must insist that $N$ be at least the $k$th prime. Topics: number theory, intersecting family. Erdős prize: $10. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_7c93ef17ba2b0184 | Erdős Problem #314 has status 'proved (lean)'. Topics: number theory, unit fractions. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_7caaf5b948754301 | Erdős Problem #1140 has been DISPROVED (a counterexample is known). Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_7cac7324cc718aeb | Erdős Problem #303 has status 'proved (lean)'. Statement: Is it true that in any finite colouring of the integers there exists a monochromatic solution to $\frac 1 a = \frac 1 b + \frac 1 c$ with distinct $a, b, c$? This is true, as proved by Brown and Rödl [BrRo91]. This was formalized in Lean by Yuan using Seed-Prover. Topics: number theory, unit fractions. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_7cb1a5b07207120e | OBLIGATION (Erdos #396). BANKED: the GPT-Pro reduction is banked and re-verified (obstruction map: HONEST, no solve). OPEN: the reduction does not solve #396; the solve remains open. | unreviewed | 0.50 | — | — | asserted · 2d |
| vf_7cd4107f21b74abf | Erdős Problem #727 remains OPEN. Statement: Let $k ≥ 2$. Does $((n+k)!)^2∣(2n)!$ hold for infinitely many $n$? Topics: number theory, factorials. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A002503, A343507, A389396. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_7d3a474b067b041f | Erdős Problem #714 remains OPEN. Topics: graph theory, turan number. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_7d42668b31967c8e | Erdős Problem #633 is SOLVED. Topics: geometry. Erdős prize: $25. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_7d46d436d8c31259 | Erdős Problem #371 remains OPEN. Statement: Let $P(n)$ denote the largest prime factor of $n$. Show that the set of $n$ with $P(n+1) > P(n)$ has density $\frac{1}{2}$. Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A070089. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_7d8cb8ee64887166 | Erdős Problem #1141 has status 'disproved (lean)'. Statement: Are there infinitely many $n$ such that $n-k^2$ is prime for all $k$ with $(n,k)=1$ and $k^2 < n$? In [Va99] it is asked whether $968$ is the largest integer with this property, but this is an error, since for example $968-9=7\cdot 137$. The list of $n$ satisfying the given property is [A214583] in the OEIS. The largest known such $n$ is $1722$. The answer is negative: [APSSV26b] proves a stronger finiteness theorem, deducing it from Pollack [Po17]. Oriike [Or26] formalised the deduction in Lean. Topics: number theory, primes. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A214583. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_7db1ad46b6bf6e2d | Erdős Problem #243 remains OPEN. Statement: Let $a_1 < a_2 < \dots$ be a sequence of integers such that $\lim_{n\to\infty} \frac{a_n}{a_{n-1}^2} = 1$ and $\sum \frac{1}{a_n} \in \mathbb{Q}$. Then, for all sufficiently large $n \ge 1$, $a_n = a_{n-1}^2 - a_{n-1} + 1$. Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A000058. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_7df1d27fba1e3d0f | Erdős Problem #698 has status 'proved (lean)'. Topics: number theory, binomial coefficients. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_7e6f45a344d5522e | Erdős Problem #115 has status 'proved (lean)'. Topics: polynomials, analysis. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_7eb38c2a00520234 | Erdős Problem #724 remains OPEN. Topics: combinatorics. Erdős prize: no. Not yet formalized in Lean. OEIS: A001438. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_7eb532bddf4560c7 | Erdős Problem #560 remains OPEN. Topics: graph theory, ramsey theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_7eba52ea8a9bc742 | OBLIGATION (Erdos #993). BANKED: the banked unimodality result for the tree/forest case verified (frozen kernel). OPEN: the general Alavi-Erdos unimodality conjecture is open. | unreviewed | 0.50 | — | — | asserted · 2d |
| vf_7ef47c30813c11b1 | Erdős Problem #109 has been PROVED (Erdős's conjecture holds). Statement: Any $A\subseteq \mathbb{N}$ of positive upper density contains a sumset $B+C$ where both $B$ and $C$ are infinite. The Erdős sumset conjecture. Proved by Moreira, Richter, and Robertson [MRR19]. Topics: additive combinatorics. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_7f70fe3b7bac107a | Erdős Problem #37 has been DISPROVED (a counterexample is known). Topics: number theory, additive combinatorics. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_7f83879b783b6f56 | Erdős Problem #1210 remains OPEN. Statement: Let $A\subseteq [1,n)$ be a set of integers such that $(a,b)=1$ for all distinct $a,b\in A$. Is it true that $\sum_{a\in A}\frac{1}{n-a}\leq \sum_{p < n}\frac{1}{p}+O(1)$? Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_800736a11cac0a13 | Erdős Problem #888 is SOLVED. Statement: What is the size of the largest subset `A` of `{1,...,n}` such that if `a ≤ b ≤ c ≤ d ∈ A` and `abcd` square then `ad=bc` Topics: number theory, squares. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A387584. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_802f4726e5bed8a2 | Erdős Problem #453 has status 'disproved (lean)'. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_805c5b2916a5339e | Erdős Problem #709 remains OPEN. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_807ae71de490f6e5 | Erdős Problem #868 is SOLVED. Topics: number theory, additive basis. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_80897a5c05f62d90 | Erdős Problem #566 remains OPEN. Statement: Let $G$ be such that any subgraph on $k$ vertices has at most $2k-3$ edges. Is it true that, if $H$ has $m$ edges and no isolated vertices, then $\hat{r}(G,H) \ll m$? In other words: if $G$ is sparse (every induced subgraph on $k$ vertices has $≤ 2k-3$ edges), is $G$ Ramsey size linear? Topics: graph theory, ramsey theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_81255c41ed6c0cd5 | Erdős Problem #1018 is SOLVED. Topics: graph theory, planar graphs. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_813eddcea38df43e | Erdős Problem #436 remains OPEN. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: A000445, possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_81c283de8cc4c934 | Erdős Problem #1119 has status 'independent'. Topics: analysis, set theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_825569afb0b04478 | Erdős Problem #1195 is SOLVED. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_825857df7e65c3ad | Erdős Problem #656 has been PROVED (Erdős's conjecture holds). Topics: number theory, additive combinatorics. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_825eec6e1a72401a | Erdős Problem #1177 remains OPEN. Topics: set theory, chromatic number, hypergraphs. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_82759dce6215e9ad | Erdős Problem #463 remains OPEN. Statement: Is there a function $f$ with $f(n)\to\infty$ as $n\to\infty$ such that, for all large $n$, there is a composite number $m$ such that $$ n + f(n) < m < n + p(m) $$ Here $p(m)$ is the least prime factor of $m$. Topics: number theory, primes. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_82910f10975ca5ab | Erdős Problem #743 has status 'falsifiable'. Topics: graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_82f4febc1a2cec5f | Erdős Problem #1207 remains OPEN. Topics: geometry, distances. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_83126944775b9ae4 | Erdős Problem #9 remains OPEN. Statement: Is the upper density of the set of odd numbers that cannot be expressed as a prime plus two powers of 2 positive? Topics: number theory, additive basis, primes. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A006286. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_831dece41da5c90c | Erdős Problem #430 remains OPEN. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_83af83f22e337973 | Erdős Problem #245 has been PROVED (Erdős's conjecture holds). Statement: Let $A\subseteq\mathbb{N}$ be an infinite set such that $|A\cap \{1, ..., N\}| = o(N)$. Is it true that $$ \limsup_{N\to\infty}\frac{|(A + A)\cap \{1, ..., N\}|}{|A \cap \{1, ..., N\}|} \geq 3? $$ The answer is yes, proved by Freiman [Fr73]. [Fr73] Fre\u{\i}man, G. A., _Foundations of a structural theory of set addition_. (1973), vii+108. Topics: additive combinatorics. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_83c63fddf141666a | Erdős Problem #1026 has status 'solved (lean)'. Topics: combinatorics. Erdős prize: no. Not yet formalized in Lean. OEIS: A391431, A391490. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_8430e53976288dc5 | Erdős Problem #1171 remains OPEN. Topics: set theory, ramsey theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_8431860ae06050de | Erdős Problem #535 remains OPEN. Statement: Let $r \geq 3$, and let $f_r(N)$ denote the size of the largest subset of $\{1,\ldots,N\}$ such that no subset of size $r$ has the same pairwise greatest common divisor between all elements. Erdős [Er64] proved that $f_3(N) > N^{c/\log\log N}$ for some constant $c > 0$, and conjectured this should also be an upper bound; here we state the conjectural upper bound for all $r \geq 3$. See also [536]. Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_84cf37caaab8677c | Erdős Problem #780 has been PROVED (Erdős's conjecture holds). Topics: combinatorics, hypergraphs, chromatic number. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_84e6f2df0ac208e4 | Erdős Problem #307 has status 'verifiable'. Statement: Are there two finite set of primes $P$ and $Q$ such that $$ 1 = \left( \sum_{p \in P} \frac{1}{p} \right) \left( \sum_{q \in Q} \frac{1}{q} \right) $$ ? Asked by Barbeau [Ba76]. [Ba76] Barbeau, E. J., _Computer challenge corner: Problem 477: A brute force program._ Topics: number theory, unit fractions. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | noted · 2d |
| vf_855ffc0d6f096ea3 | Erdős Problem #844 has status 'proved (lean)'. Topics: number theory, intersecting family. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_8569dabb2be4c23b | Erdős Problem #1011 remains OPEN. Topics: graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_8572156c15e89385 | Erdős Problem #380 has been PROVED (Erdős's conjecture holds). Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: A070003, A388654, A387054, A389100. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_859ba34fadee07e9 | Erdős Problem #589 remains OPEN. Topics: geometry. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_859d002cbfedc2dc | Erdős Problem #308 has been PROVED (Erdős's conjecture holds). Topics: number theory, unit fractions. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_85dafb41335ec3d5 | Erdős Problem #216 has been DISPROVED (a counterexample is known). Topics: geometry, convex. Erdős prize: no. Not yet formalized in Lean. OEIS: A381776. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_8636a3d52884c5bd | Erdős Problem #206 has status 'disproved (lean)'. Topics: number theory, unit fractions. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_864d6a05c53a3a94 | Erdős Problem #751 has status 'disproved (lean)'. Topics: graph theory, chromatic number. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_867f80e615ebffd0 | Erdős Problem #1151 remains OPEN. Topics: analysis, polynomials. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_86bd4d8d2fc4667b | Erdős Problem #511 has been DISPROVED (a counterexample is known). Topics: analysis. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_86ca5c0e4d892c9a | Erdős Problem #542 is SOLVED. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_86ebc476908ca443 | Erdős Problem #1133 remains OPEN. Topics: analysis, polynomials. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_870f6be42ee8bf9f | Erdős Problem #523 has been PROVED (Erdős's conjecture holds). Topics: analysis, probability, polynomials. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_8753f671ba918f3f | Erdős Problem #363 has status 'disproved (lean)'. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_87595279cb9eda1e | Erdős Problem #66 remains OPEN. Statement: Is there and $A \subset \mathbb{N}$ is such that $$\lim_{n\to \infty}\frac{1_A\ast 1_A(n)}{\log n}$$ exists and is $\ne 0$? Topics: number theory, additive basis. Erdős prize: $500. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_87911aed1e2cf079 | Erdős Problem #693 remains OPEN. Topics: number theory, divisors. Erdős prize: no. Not yet formalized in Lean. OEIS: A391118, possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_87a1ab0706b8129b | Erdős Problem #820 remains OPEN. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: A263647. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_87ccf2774c2ed706 | Erdős Problem #338 remains OPEN. Topics: number theory, additive basis. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_880d801a386867b1 | Erdős Problem #944 remains OPEN. Statement: Let $k \ge 4$ and $r\ge 1$. Must there exist a graph $G$ with chromatic number $k$ such that every vertex is critical, yet every critical set of edges has size $>r$? Topics: graph theory, chromatic number. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_8847971758e968de | Erdős Problem #370 has status 'proved (lean)'. Statement: Are there infinitely many $n$ such that the largest prime factor of $n$ is $< n^{\frac{1}{2}}$ and the largest prime factor of $n + 1$ is $< (n + 1)^{\frac{1}{2}}$. Steinerberger has pointed out this problem has a trivial solution. This was formalized in Lean by Alexeev using Aristotle. Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_88707054a3df53d3 | Erdős Problem #490 has status 'proved (lean)'. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_88e9c72c825c6e93 | Erdos distinct distances problem (1946 conjecture, essentially solved by Guth-Katz 2010): n points in the plane determine at least Omega(n / log n) distinct pairwise distances, matching Erdos's lattice-construction upper bound up to log factors. | unreviewed | 0.95 | — | — | asserted · 13d |
| vf_88fd0021b4a1a98b | Erdős Problem #994 has been DISPROVED (a counterexample is known). Topics: analysis, discrepancy. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_890bee5571d47674 | Erdős Problem #559 has been DISPROVED (a counterexample is known). Topics: graph theory, ramsey theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_891e84925bd8d975 | Erdős Problem #573 remains OPEN. Topics: graph theory, turan number. Erdős prize: no. Not yet formalized in Lean. OEIS: A006856. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_8a0007614b040743 | Erdős Problem #556 has status 'decidable'. Topics: graph theory, ramsey theory. Erdős prize: no. Not yet formalized in Lean. OEIS: A389335. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_8a36bcd1cf62278f | Erdős Problem #389 remains OPEN. Statement: Is it true that for every $n \geq 1$ there is a $k$ such that $$ n(n + 1) \cdots (n + k - 1) \mid (n + k) \cdots (n + 2k - 1)? $$ Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A375071. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_8a45209177f1af22 | Erdős Problem #1001 is SOLVED. Topics: number theory, diophantine approximation. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_8a86aa132defee78 | Erdős Problem #563 remains OPEN. Topics: graph theory, ramsey theory, hypergraphs. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_8ab1cec60f1b4833 | Erdős Problem #917 remains OPEN. Topics: graph theory, chromatic number. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_8b8530cbf813c02a | Erdős Problem #122 remains OPEN. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_8b85ef50f5aabb8d | Erdős Problem #645 has status 'proved (lean)'. Statement: If ℕ is $2$-coloured then there must exist a monochromatic three-term arithmetic progression $x,x+d,x+2d$ such that $d>x$. This was first proved by Brown and Landman [BrLa99], who in fact show that this is always possible with $d>f(x)$ for any increasing function $f$. This was formalized in Lean by Alexeev using Aristotle and ChatGPT. Topics: number theory, additive combinatorics, ramsey theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_8b9286cae0885675 | Erdős Problem #588 remains OPEN. Topics: geometry. Erdős prize: $100. Not yet formalized in Lean. OEIS: A006065, A008997. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_8ba54b849fb51384 | Erdős Problem #127 has been PROVED (Erdős's conjecture holds). Topics: graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_8bc42bb08f70dd3f | Erdős Problem #1153 has been PROVED (Erdős's conjecture holds). Topics: analysis, polynomials. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_8c30b75ba4c41ff0 | Erdős Problem #839 remains OPEN. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_8cd48f0900479982 | Erdős Problem #584 remains OPEN. Topics: graph theory, cycles. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_8d3507a25bb6d16c | Erdős Problem #767 has been PROVED (Erdős's conjecture holds). Topics: graph theory, turan number. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_8d5ada8b450f91ca | Erdős Problem #138 remains OPEN. Statement: In [Er80] Erdős asks whether $$ \lim_{k \to \infty} (W(k))^{1/k} = \infty $$ Topics: additive combinatorics. Erdős prize: $500. Statement is machine-verified in Lean (formal-conjectures). OEIS: A005346. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_8d8da581a9b4757b | Erdős Problem #1070 remains OPEN. Topics: geometry. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_8de89353949bdeee | Erdős Problem #251 remains OPEN. Statement: Is $\sum_{n=1}^\infty \frac{p_n}{2^n}$ irrational? Here $p_n$ is the $n$-th prime ($p_1=2, p_2=3, \dots$). Topics: number theory, irrationality. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A098990. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_8e166486c13046d3 | Erdős Problem #124 remains OPEN. Topics: number theory, base representations. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_8e95bb291f60a6f4 | Erdős Problem #758 is SOLVED. Topics: graph theory, chromatic number. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_8ea663a3d8f98a68 | Erdős Problem #896 is SOLVED. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_8ef1cb121aec1108 | Erdős Problem #21 has been PROVED (Erdős's conjecture holds). Topics: combinatorics, intersecting family. Erdős prize: $500. Not yet formalized in Lean. OEIS: A391599. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_8f3ee6c74f9e955e | Erdős Problem #272 remains OPEN. Statement: Let $N\geq 1$. What is the largest $t$ such that there are $A_1,\ldots,A_t\subseteq \{1,\ldots,N\}$ with $A_i\cap A_j$ a non-empty arithmetic progression for all $i\neq j$? Topics: additive combinatorics, arithmetic progressions. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_8fdc77a59a1c9f1e | Erdős Problem #246 has status 'proved (lean)'. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_8fdce4bf9419e970 | Erdős Problem #564 remains OPEN. Statement: Let $R_3(n)$ be the minimal $m$ such that if the edges of the $3$-uniform hypergraph on $m$ vertices are $2$-coloured then there is a monochromatic copy of the complete $3$-uniform hypergraph on $n$ vertices. Is there some constant $c>0$ such that $$ R_3(n) \geq 2^{2^{cn}}? $$ Topics: graph theory, ramsey theory, hypergraphs. Erdős prize: $500. Statement is machine-verified in Lean (formal-conjectures). OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_8ff17505900023c7 | Erdős Problem #909 has been PROVED (Erdős's conjecture holds). Topics: analysis, topology. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_901cb57486bbf73d | Erdős Problem #29 has been PROVED (Erdős's conjecture holds). Topics: number theory, additive basis. Erdős prize: $100. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_902773d698f748c9 | Erdős Problem #548 has status 'falsifiable'. Topics: graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_912ea88190378ef3 | Erdős Problem #75 remains OPEN. Statement: Is there a graph of chromatic number `ℵ_ 1` with `ℵ_ 1` vertices such that for all `ε > 0`, if `n` is sufficiently large and `H` is a subgraph on `n` vertices, then `H` contains an independent set of size `> n ^ (1 - ε)`? Topics: graph theory, chromatic number. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_9190e67826cbfeb8 | Erdős Problem #413 remains OPEN. Topics: number theory, iterated functions. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A005236. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_919f579bba9dd797 | Erdős Problem #630 has been PROVED (Erdős's conjecture holds). Topics: graph theory, chromatic number. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_91aabdf662b9b148 | Erdős Problem #423 remains OPEN. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: A005243. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_91b111b200746815 | Erdős Problem #211 has been PROVED (Erdős's conjecture holds). Topics: geometry. Erdős prize: $100. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_91c714036b80b03b | Erdős Problem #1083 remains OPEN. Topics: geometry, distances. Erdős prize: no. Not yet formalized in Lean. OEIS: A186704, possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_91cff8684f60c583 | Erdős Problem #775 has status 'disproved (lean)'. Topics: graph theory, hypergraphs. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_924e06017f2df610 | Erdős Problem #282 remains OPEN. Statement: Let $A\subseteq \mathbb{N}$ be an infinite set and consider the following greedy algorithm for a rational $x\in (0,1)$: choose the minimal $n\in A$ such that $n\geq 1/x$ and repeat with $x$ replaced by $x-\frac{1}{n}$. If this terminates after finitely many steps then this produces a representation of $x$ as the sum of distinct unit fractions with denominators from $A$. Does this process always terminate if $x$ has odd denominator and $A$ is the set of odd numbers? Topics: number theory, unit fractions. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_92515ff2ca77cf09 | Erdős Problem #1081 has been DISPROVED (a counterexample is known). Topics: number theory, powerful. Erdős prize: no. Not yet formalized in Lean. OEIS: A076871, A076872, possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_9252f9e9f5b28a21 | Erdős Problem #515 has been PROVED (Erdős's conjecture holds). Topics: analysis. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_926d67a55d326147 | Erdős Problem #192 has status 'solved (lean)'. Topics: arithmetic progressions, combinatorics. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_92737f5c1202924e | Erdős Problem #984 has been PROVED (Erdős's conjecture holds). Topics: arithmetic progressions, additive combinatorics. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_92e916d528288b17 | Erdős Problem #772 has been PROVED (Erdős's conjecture holds). Topics: number theory, sidon sets, additive combinatorics. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_935b50123a3ea76a | Erdős Problem #323 remains OPEN. Topics: number theory, powers. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_935cc2b5848ffe43 | Erdős Problem #826 remains OPEN. Statement: Are there infinitely many $n$ such that, for all $k\geq 1$ $$ \tau(n + k) \ll k? $$ Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_9361c940b7e41832 | Erdős Problem #330 has status 'proved (lean)'. Topics: number theory, additive basis. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_9394feefcdd48267 | Erdős Problem #752 has been PROVED (Erdős's conjecture holds). Topics: graph theory, cycles. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_93b24c34107dc3ac | Erdős Problem #1104 remains OPEN. Topics: graph theory, chromatic number. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A292528. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_9401deb108043ad3 | Erdős Problem #51 remains OPEN. Statement: Is there an infinite set $A \subset \mathbb{N}$ such that for every $a \in A$, there is an integer n such that $\phi(n)=a$, and yet if $n_a$ is the smallest such integer, then $\frac{n_a}{a} → \infty$ as $a → ∞$? Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A002202, A014197. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_94250d1cf1250c7f | Erdős Problem #177 remains OPEN. Topics: discrepancy, arithmetic progressions. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_94480287b31ddabc | Erdős Problem #940 remains OPEN. Statement: Let $r \ge 3$. Is it true that the set of integers which are the sum of at most $r$ $r$-powerful numbers has density $0$? Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_944c150e1e50ae0f | Erdős Problem #782 remains OPEN. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_94664fd00db02fc3 | Erdős Problem #774 remains OPEN. Statement: Is every proportionately dissociated (infinite) set the union of a finite number of dissociated sets? Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_946fdc2fab352bc0 | Erdős Problem #850 remains OPEN. Statement: Can there exist two distinct integers $x$ and $y$ such that $x,y$ have the same prime factors, $x+1,y+1$ have the same prime factors, and $x+2,y+2$ also have the same prime factors? Topics: number theory, primes. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A343101. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_9488e94315642e8a | Erdős Problem #845 has status 'disproved (lean)'. Statement: Let $C > 0$. Is it true that the set of integers of the form $n = b_1 + \cdots + b_t$, with $b_1 < \cdots < b_t$, where $b_i = 2^{k_i}3^{l_i}$ for $1 \leq i\leq t$ and $b_t \leq Cb_1$ has density $0$? van Doorn and Everts \cite{vDEv25} have disproved this with $C=6$ - in fact, they prove that all integers can be written as such a sum in which $b_t<6b_1$. This was formalized in Lean by Alexeev using Aristotle. Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_949acd38056f0fa6 | Erdős Problem #348 remains OPEN. Statement: For what values of $0 \leq m < n$ is there a complete sequence $A = \{a_1 \leq a_2 \leq \cdots\}$ of integers such that 1. $A$ remains complete after removing any $m$ elements, but 2. $A$ is not complete after removing any $n$ elements. Topics: number theory, complete sequences. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_94e460f5e0cb9c48 | Erdős Problem #27 has been DISPROVED (a counterexample is known). Topics: number theory, covering systems. Erdős prize: $100. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_9504701effc21d15 | Erdős Problem #609 remains OPEN. Topics: graph theory, ramsey theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_9516e097b07e096b | Erdős Problem #1174 has status 'not disprovable'. Topics: set theory, ramsey theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_963ca7ac8bfff3d1 | Erdős Problem #1131 remains OPEN. Topics: analysis, polynomials. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_9644bea9d4f359a3 | Erdős Problem #431 remains OPEN. Topics: number theory, primes. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_964e07212f5d6b57 | Erdos-Ko-Rado theorem (1961, solved): for n >= 2k, the largest intersecting family of k-element subsets of {1,...,n} has size C(n-1, k-1) and consists of all k-sets containing a fixed element. | unreviewed | 0.95 | — | — | asserted · 13d |
| vf_9656f94c3876cf0a | Erdős Problem #571 remains OPEN. Topics: graph theory, turan number. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_96bbfb9b7ff9fe33 | Erdős Problem #1089 is SOLVED. Topics: geometry, distances. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_96fc24d2068bcd3b | Erdős Problem #950 remains OPEN. Topics: number theory, primes. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_973fbc20718802af | Erdős Problem #191 has been PROVED (Erdős's conjecture holds). Topics: combinatorics, ramsey theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_974e6b9472d2da2e | Erdős Problem #125 has status 'disproved (lean)'. Statement: Case 3: Does $A + B$ have positive upper and lower density that are equal? This is the literal interpretation of "positive density" which was falsified. Topics: number theory, base representations. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A367090. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_977117abf11df823 | Erdős Problem #762 has status 'disproved (lean)'. Topics: graph theory, chromatic number. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_977e084702bfa588 | Erdős Problem #256 remains OPEN. Topics: analysis. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_97b1edf68d581936 | Erdős Problem #69 has been PROVED (Erdős's conjecture holds). Statement: Is $$ \sum_{n\geq 2}\frac{\omega(n)}{2^n} $$ irrational? (Here $\omega(n)$ counts the number of distinct prime divisors of $n$.) Topics: number theory, irrationality. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A262153. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_97b7940ca839ad3a | Erdős Problem #794 has status 'disproved (lean)'. Topics: graph theory, hypergraphs, turan number. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_97d811ac5f392e6f | Erdős Problem #202 has status 'solved (lean)'. Topics: covering systems. Erdős prize: no. Not yet formalized in Lean. OEIS: A389975. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_97e16ecc5fd526ae | Erdős Problem #660 remains OPEN. Topics: geometry, distances, convex. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_980ccc03b462603d | Erdős Problem #22 has been PROVED (Erdős's conjecture holds). Topics: graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_98478e05babb8fb3 | Erdos-Posa theorem (1965, solved): for every k, there is a function f such that every graph either contains k vertex-disjoint cycles or has a feedback vertex set of size at most f(k); f(k) = O(k log k) is tight. | unreviewed | 0.95 | — | — | asserted · 13d |
| vf_99175f4cbd606171 | Erdős Problem #768 remains OPEN. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: A001034, A352287. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_9922ef5bd85c8f2a | Erdős Problem #352 remains OPEN. Statement: Is there some $c > 0$ such that every measurable $A \subseteq \mathbb{R}^2$ of measure $\geq c$ contains the vertices of a triangle of area 1? Topics: geometry. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_993903a9cd612c0b | Erdős Problem #359 remains OPEN. Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A002048. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_99812ef5dda0582f | Erdős Problem #410 remains OPEN. Statement: Let $σ_1(n) = σ(n)$, the sum of divisors function, and $σ_k(n) = σ(σ_{k-1}(n))$. Is it true that $\lim_{k → ∞} σ_k(n)^{\frac 1 k} = ∞$? This is problem (iii) from Erdos, Granville, Pomerance, Spiro "On the normal behavior of the iterates of some arithmetical functions" (page 169 of the book "Analytic Number Theory", 1990). Topics: number theory, iterated functions. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A007497, possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_9a08b25a84240448 | Erdős Problem #708 remains OPEN. Topics: number theory. Erdős prize: $100. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_9a8268441eeea0e4 | Erdős Problem #878 remains OPEN. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: A339378, possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_9aae8076453a57b9 | Erdős Problem #522 remains OPEN. Statement: Let $f(z)=\sum_{0\leq k\leq n} \epsilon_k z^k$ be a random polynomial, where $\epsilon_k\in \{-1,1\}$ independently uniformly at random for $0\leq k\leq n$. Is it true that, if $R_n$ is the number of roots of $f(z)$ in $\{ z\in \mathbb{C} : \lvert z\rvert \leq 1\}$, then $$ \frac{R_n}{n/2}\to 1 $$ almost surely? There is some ambiguity as to whether the intended coefficient set is $\{-1, 1\}$ or $\{0, 1\}$, see `erdos_522.variants.zero_one` for the alternate version. Topics: analysis, polynomials, probability. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_9ada63461d30a037 | Erdős Problem #978 remains OPEN. Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_9aea98072acbe829 | Erdős Problem #533 has been DISPROVED (a counterexample is known). Topics: graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_9afd681da41bbc6f | Erdős Problem #200 remains OPEN. Statement: Does the longest arithmetic progression of primes in $\{1,\ldots,N\}$ have length $o(\log N)$? Topics: primes, arithmetic progressions. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A005115. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_9b39406ea761804f | Erdős Problem #123 remains OPEN. Statement: **Erdős Problem #123** Let $a, b, c$ be three integers which are pairwise coprime. Is every large integer the sum of distinct integers of the form $a^k b^l c^m$ ($k, l, m ≥ 0$), none of which divide any other? Equivalently: is the set $\{a^k b^l c^m : k, l, m \geq 0\}$ d-complete? Note: For this not to reduce to the two-integer case, we need the integers to be greater than one and distinct. Topics: number theory. Erdős prize: $250. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_9b42f1d27f74ada4 | Erdős Problem #1200 remains OPEN. Topics: number theory, primes. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_9b460ba7474a8037 | Erdős Problem #1033 remains OPEN. Topics: graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_9b7a73c7381508d9 | Erdős Problem #981 has been PROVED (Erdős's conjecture holds). Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_9ba786be99faffa2 | Erdős Problem #1093 remains OPEN. Topics: number theory, binomial coefficients. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | noted · 2d |
| vf_9c24b7ea8ed0aca2 | Erdős Problem #1118 is SOLVED. Topics: analysis. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_9c62b464f74dfcdf | Erdős Problem #622 has been PROVED (Erdős's conjecture holds). Topics: graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_9ce8fdd169420838 | Erdős Problem #735 is SOLVED. Topics: geometry. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_9d2c363084136dd6 | Erdős Problem #335 remains OPEN. Topics: number theory, additive combinatorics. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_9d7fa690db7adfd9 | Erdős Problem #962 remains OPEN. Statement: Main conjecture: $\log k(n) \le (\log n)^{(1/2 + o(1))}$ Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A327909. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_9d981d629f64c6b7 | Erdős Problem #470 remains OPEN. Topics: number theory, divisors. Erdős prize: $10. Statement is machine-verified in Lean (formal-conjectures). OEIS: A006037, A002975. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_9dc909c5700df6b4 | Erdős Problem #1090 has status 'proved (lean)'. Topics: geometry, ramsey theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_9e0543dd7357caf2 | Erdős Problem #89 remains OPEN. Statement: Does every set of $n$ distinct points in $\mathbb{R}^2$ determine $\gg \frac{n}{\sqrt{\log n}}$ many distinct distances? Topics: geometry, distances. Erdős prize: $500. Statement is machine-verified in Lean (formal-conjectures). OEIS: A186704, A131628. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_9e28c1023d4edd6c | Erdős Problem #458 has status 'falsifiable'. Statement: Let $\operatorname{lcm}(1, \dots, n)$ denote the least common multiple of $\{1, \dots, n\}$. Let $p_k$ be the $k$-th prime. Is it true that for all $k \geq 1$, $\operatorname{lcm}(1, \dots, p_{k+1}-1) < p_k \cdot \operatorname{lcm}(1, \dots, p_k)$? Topics: number theory, primes. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A056604. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_9e571c292bedde14 | Erdős Problem #846: machine-found Lean proof published by AlphaProof Nexus (DeepMind, arXiv 2605.22763, May 2026). Independently re-verified locally 2026-06-10: full lake build of google-deepmind/alphaproof-nexus-results@0647711a7118 under their pinned toolchain leanprover/lean4:v4.27.0 succeeded (8062 jobs); static scan clean (no sorry, no native_decide, no custom axioms). Artifacts: erdos_846.lean sha256:47f77fbc9646be4c. AI involvement: machine-generated proof, machine-checked (Lean kernel is the referee); statement faithfulness NOT yet independently attested — see paper section 4 for DeepMind's own expert validation. | unreviewed | 0.90 | — | — | attested · 2d |
| vf_9ee71a3bfa821903 | Erdős Problem #596 remains OPEN. Topics: graph theory, ramsey theory, set theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_9efa322ce4c4ce37 | Erdős Problem #985 remains OPEN. Statement: Is it true that, for every prime $p$, there is a prime $q \leq p$ which is a primitive root modulo $p$? Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A002233, A219429, A103309, possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_9eff5f5697894e6d | Erdős Problem #514 remains OPEN. Topics: analysis. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_9f04f9669b5b7388 | Erdős Problem #10 remains OPEN. Statement: Is there some $k$ such that every integer is the sum of a prime and at most $k$ powers of $2$? Topics: number theory, additive basis, primes. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A387053. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_9f05b88acfc88384 | Erdős Problem #1150 remains OPEN. Statement: Is there some constant $c > 0$ such that, for all large enough $n$ and all polynomials $P$ of degree $n$ with coefficients in $\{-1, 1\}$, $$\max_{|z|=1} |P(z)| > (1 + c) \sqrt{n}?$$ Topics: analysis, polynomials. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_a001a009700ec1a0 | Erdős Problem #553 has been PROVED (Erdős's conjecture holds). Topics: graph theory, ramsey theory. Erdős prize: no. Not yet formalized in Lean. OEIS: A000791, possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_a01e30d8b023a5dc | Erdős Problem #1045 remains OPEN. Topics: analysis. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_a0cd5086d32f16a4 | Erdős Problem #956 remains OPEN. Topics: geometry, distances, convex. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_a0eeea14152e3bcf | Erdős Problem #550 remains OPEN. Topics: graph theory, ramsey theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_a109db7281d43812 | Erdős Problem #403 has been PROVED (Erdős's conjecture holds). Topics: number theory, factorials. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_a18c81be0ce3819d | Erdős Problem #869 has been DISPROVED (a counterexample is known). Topics: number theory, additive basis. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_a1ca0137568f41a4 | Erdős Problem #541 has status 'proved (lean)'. Statement: Let $a_1, \dots, a_p$ be (not necessarily distinct) residues modulo a prime $p$, such that there exists some $r$ so that if $S \subseteq [p]$ is non-empty and $$\sum_{i \in S} a_i \equiv 0 \pmod{p}$$ then $|S| = r$. Must there be at most two distinct residues amongst the $a_i$? This was formalized in Lean by Alexeev using Aristotle and ChatGPT. Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_a1e06130f1d49d33 | Erdős Problem #244 remains OPEN. Statement: Let $C > 1$. Does the set of integers of the form $p + \lfloor C^k \rfloor$, for some prime $p$ and $k\geq 0$, have density $>0$? Topics: number theory, primes. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_a1e20cfb6d095c10 | Erdős Problem #691 remains OPEN. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_a28141356a6e7f45 | Erdős Problem #179 has been PROVED (Erdős's conjecture holds). Topics: additive combinatorics, arithmetic progressions. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_a2d087e9bbd86e6c | Erdős Problem #269 remains OPEN. Topics: irrationality. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_a2e5b2176767bd6a | Erdős Problem #141 remains OPEN. Statement: Let $k≥3$. Are there $k$ consecutive primes in arithmetic progression? Topics: additive combinatorics, primes, arithmetic progressions. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A006560. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_a2edaf53d1a4f367 | Erdős Problem #409 remains OPEN. Topics: number theory, iterated functions. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A039651, A229487. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_a31297cad5ba8f20 | Erdős Problem #607 has been PROVED (Erdős's conjecture holds). Topics: geometry. Erdős prize: $250. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_a335293497fd9b2a | Erdős Problem #93 has status 'proved (lean)'. Topics: geometry, convex, distances. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_a33ada9849c02136 | Erdős Problem #821 remains OPEN. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: A014197. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_a3424c338522cb4b | Erdős Problem #884 has been DISPROVED (a counterexample is known). Statement: For a natural number n, let $1 = d_1 < \dotsc < d_{\tau(n)} = n$ denote the divisors of $n$ in increasing order. Does it hold that $\sum_{1 \le i < j \le \tau(n)} \frac{1}{d_j - d_i} \ll 1 + \sum_{1 \le i < \tau(n)} \frac{1}{d_{i + 1} - d_i}$ for $n \to \infty`, i.e. $\sum_{1 \le i < j \le \tau(n)} \frac{1}{d_j - d_i} \in O \left( 1 + \sum_{1 \le i < \tau(n)} \frac{1}{d_{i + 1} - d_i}) \right)$? This conjecture has been **disproved**: - In September 2025, Terence Tao gave a conditional _negative_ answer assuming the prime tuples conjecture, see `erdos_884_false_of_hardy_littlewood` for this implication. - Daniel Larsen subsequently gave an [unconditional disproof](https://github.com/Larsen-Daniel/Erdos-884/blob/main/884.pdf). *Reference:* [erdosproblems.com/884](https://www.erdosproblems.com/884) Topics: number theory, divisors. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_a357c9d8ac3d6b26 | Erdős Problem #44 remains OPEN. Statement: **Erdős Problem 44:** Let N ≥ 1 and `A ⊆ {1,…,N}` be a Sidon set. Is it true that, for any ε > 0, there exist M = M(ε) and `B ⊆ {N+1,…,M}` such that `A ∪ B ⊆ {1,…,M}` is a Sidon set of size at least `(1−ε)M^{1/2}`? This problem asks whether any Sidon set can be extended to achieve a density arbitrarily close to the optimal density for Sidon sets. Topics: number theory, sidon sets, additive combinatorics. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_a35eee5139b961b7 | Erdős Problem #866 remains OPEN. Topics: number theory, additive combinatorics. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_a3bd44e08f7d2ce0 | Erdős Problem #865 remains OPEN. Statement: There exists a constant $C>0$ such that, for all large $N$, if $A\subseteq \{1,\ldots,N\}$ has size at least $\frac{5}{8}N+C$ then there are distinct $a,b,c\in A$ such that $a+b,a+c,b+c\in A$. A problem of Erdős and Sós (also earlier considered by Choi, Erdős, and Szemerédi [CES75], but Erdős had forgotten this). Topics: number theory, additive combinatorics. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_a46bc3d62cb5ee4e | Erdős Problem #205 has status 'disproved (lean)'. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_a5304068ccb0e15c | Erdős Problem #841 is SOLVED. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: A092487. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_a566be23717e9a21 | Erdős Problem #1051 has status 'proved (lean)'. Statement: Is it true that if $a_0 < a_1 < a_2 < \cdots$ is a strictly increasing sequence of integers with $\liminf a_n^{1/2^n} > 1$, then the series $\sum_{n=0}^\infty \frac{1}{a_n \cdot a_{n+1}}$ is irrational? This was solved in the affirmative by Aletheia [Fe26]. This was extended by Barreto, Kang, Kim, Kovač, and Zhang [BKKKZ26], who essentially give a complete answer: if $\phi=\frac{1+\sqrt{5}}{2}$ is the golden ratio and $1\leq a_1 < a_2 < \cdots$ is a monotonically increasing sequence of integers such that $\limsup a_n^{1/\phi^{n}}=\infty$ then $\sum_{n=1}^\infty \frac{1}{a_na_{n+1}}$ is irrational. Conversely, for any $1 < C < \infty$ there exists a sequence of integers $1\leq a_1<\cdots$ such that $\lim a_n^{1/\phi^{n}}=C$ where this infinite sum is a rational number. (Further, more general, results are available in [BKKKZ26].) This was formalized in Lean by Baretto. Topics: irrationality. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_a58c00383158f48b | Erdős Problem #581 is SOLVED. Topics: graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_a5a5f9fdd6ed6430 | Erdős Problem #885 remains OPEN. Statement: Is it true that, for every $k \geq 1$, there exist integers $N_1 < \dots < N_k$ such that $|\cap_i D(N_i)| \geq k$? Topics: number theory, divisors. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_a5b5914c52ede11e | Erdős Problem #415 remains OPEN. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_a5d6012b84789ece | Erdős Problem #1015 is SOLVED. Topics: graph theory, ramsey theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_a5d6ba4ed7fad752 | Erdős Problem #67 has been PROVED (Erdős's conjecture holds). Statement: **The Erdős discrepancy problem** If $f\colon \mathbb N \rightarrow \{-1, +1\}$ then is it true that for every $C>0$ there exist $d, m \ge 1$ such that $$\left\lvert \sum_{1\leq k\leq m}f(kd)\right\rvert > C?$$ This is true, and was proved by Tao [Ta16] Topics: discrepancy. Erdős prize: $500. Statement is machine-verified in Lean (formal-conjectures). OEIS: A181740, A237695. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_a5fdcc6638ecec0c | Erdős Problem #717 has been PROVED (Erdős's conjecture holds). Topics: graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_a65af9929d8f2cd4 | Erdős Problem #361 remains OPEN. Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_a67df8d364c1dc93 | Erdős Problem #18 remains OPEN. Topics: number theory, divisors, factorials. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A005153. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_a67f1c96bc41e640 | Erdős Problem #181 remains OPEN. Topics: graph theory, ramsey theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_a68f2aaf069dc674 | Erdős Problem #828 remains OPEN. Statement: Is it true that, for any $a \in \mathbb{Z}$, there are infinitely many $n$ such that $$\phi(n) | n + a$$? Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_a7288a8b21ac6798 | Erdős Problem #273 remains OPEN. Statement: Is there a covering system all of whose moduli are of the form $p-1$ for some primes $p \geq 5$? Topics: number theory, covering systems. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_a72e7004f4b553ab | Erdős Problem #418 has status 'proved (lean)'. Statement: Are there infinitely many integers not of the form $n - \phi(n)$? Asked by Erdős and Sierpiński. Numbers not of the form we call non-cototients. Browkin and Schinzel [BrSc95] provided an affirmative answer to this question, proving that any integer of the shape $2^{k}\cdot 509203$ for $k\geq 1$ is a non-cototient. This is discussed in problem B36 of Guy's collection [Gu04]. This was formalized in Lean by Alexeev using Aristotle. Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A005278, A263958. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_a769896594a6d627 | Erdős Problem #235 has been PROVED (Erdős's conjecture holds). Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_a78636c24e39f58a | Erdős Problem #8 has been DISPROVED (a counterexample is known). Topics: number theory, covering systems. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_a799eda095525e0e | Erdős Problem #653 remains OPEN. Statement: Let $x_1,\ldots,x_n\in \mathbb{R}^2$ and let $R(x_i)=\#\{ \lvert x_j-x_i\rvert : j\neq i\}$, where the points are ordered such that $$R(x_1)\leq \cdots \leq R(x_n).$$ Let $g(n)$ be the maximum number of distinct values the $R(x_i)$ can take. Is it true that $g(n) \geq (1-o(1))n$? Topics: geometry, distances. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_a7a0281b40430276 | Erdős Problem #419 has status 'solved (lean)'. Topics: number theory, factorials. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_a8089d3e70d544dc | Erdős Problem #1058 has been PROVED (Erdős's conjecture holds). Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_a80ac0e6af97f8b1 | Erdős Problem #650 has status 'solved (lean)'. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: A027434. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_a8aeab09d61cc304 | Erdős Problem #422 remains OPEN. Statement: Does $f(n)$ miss infinitely many integers? Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A005185. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_a8f7162df54cd58f | Erdős Problem #193 remains OPEN. Statement: Let $S \subseteq \mathbb{Z}^3$ be a finite set and let $A = \lbrace a_1, a_2, \ldots \rbrace$ be an infinite $S$-walk, so that $a_{i+1} - a_i \in S$ for all $i$. Must $A$ contain three collinear points? Topics: geometry. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A231255. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_a8fab4b7d1d7cb28 | Erdős Problem #279 remains OPEN. Statement: Let $k\geq 3$. Is there a choice of congruence classes $a_p\pmod{p}$ for every prime $p$ such that all sufficiently large integers can be written as $a_p+tp$ for some prime $p$ and integer $t\geq k$? Topics: number theory, covering systems, primes. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_a93c2502fd730adc | Erdős Problem #162 remains OPEN. Topics: combinatorics, ramsey theory, discrepancy. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_a9626db2e57d5549 | Erdős Problem #846 has status 'disproved (lean)'. Statement: **Erdős Problem 846** Let `A ⊂ ℝ²` be an infinite set for which there exists some `ϵ>0` such that in any subset of `A` of size `n` there are always at least `ϵn` with no three on a line. Is it true that `A` is the union of a finite number of sets where no three are on a line? In other words, prove or disprove the following statement: every infinite `ε`-non-trilinear subset of the plane is weakly non-trilinar. Topics: geometry. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_a971a61ad2178fe2 | Erdős Problem #543 has been DISPROVED (a counterexample is known). Topics: number theory, group theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_a9a5b1e0dbdc9da4 | OBLIGATION (Erdos #319). BANKED: the counting step of the upper bound corroborated numerically. OPEN: the full upper bound is not established by the numerics alone. | unreviewed | 0.50 | — | — | asserted · 2d |
| vf_a9ec3a6f173b434e | Erdős Problem #685 remains OPEN. Topics: number theory, primes, binomial coefficients. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_aa0ab55d77b62211 | Erdős Problem #644 remains OPEN. Topics: combinatorics. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_aaa4550785c434ab | Erdős Problem #13 has been PROVED (Erdős's conjecture holds). Statement: If $A \subseteq \{1, ..., N\}$ is a set with no $a, b, c \in A$ such that $a | (b+c)$ and $a < \min(b,c)$, then $|A| \le N/3 + O(1)$. This has been solved by Bedert [Be23]. [Be23] Bedert, B., _On a problem of Erdős and Sárközy about sequences with no term dividing the sum of two larger terms_. arXiv:2301.07065 (2023). Topics: number theory. Erdős prize: $100. Statement is machine-verified in Lean (formal-conjectures). OEIS: A002264. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_aabfe3f3c9176f96 | Erdős Problem #670 remains OPEN. Topics: geometry, distances. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_ab4e2145e463abb4 | Erdős Problem #19 has status 'decidable'. Topics: graph theory, chromatic number. Erdős prize: $500. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_ab6e620f701aa23a | Erdős Problem #873 remains OPEN. Statement: Let $A = \{a_1 < a_2 < \dots\} \subseteq \mathbb{N}$ and let $F(A,X,k)$ count the number of $i$ such that $[a_i,a_{i+1}, \dots ,a_{i+k−1}] < X$, where the left-hand side is the least common multiple. Is it true that, for every $\epsilon > 0$, there exists some $k$ such that $F(A,X,k) < X^\epsilon$? Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_ab97596d867a4193 | Erdős Problem #946 has been PROVED (Erdős's conjecture holds). Statement: There are infinitely many $n$ such that $τ(n) = τ(n+1)$. Proved in [He84]. Here τ is the divisor counting function, which is `σ 0` in mathlib. Topics: number theory, divisors. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A005237, A284783. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_ac138f62d2af876e | Erdős Problem #823 has been PROVED (Erdős's conjecture holds). Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_ac4c84ea5e608bb7 | OBLIGATION (Erdos #647). BANKED: the prime / forced-divisor channel is provably exhausted (banked obstruction_map + Erdos647Obstruction.lean). OPEN: a different channel is required; the prime channel cannot close it (stop grinding it). | unreviewed | 0.50 | — | — | asserted · 2d |
| vf_ac5f19ba93429d33 | Erdos-Szekeres theorem (1935, solved): every sequence of (r-1)(s-1)+1 distinct real numbers contains a monotone increasing subsequence of length r or a monotone decreasing subsequence of length s. | unreviewed | 0.95 | — | — | asserted · 13d |
| vf_ac64eb8e81f9b57b | Erdős Problem #765 has status 'solved (lean)'. Topics: graph theory, turan number. Erdős prize: no. Not yet formalized in Lean. OEIS: A006855. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_ac6f7fd217e02f24 | Erdős Problem #322 remains OPEN. Topics: number theory, powers. Erdős prize: no. Not yet formalized in Lean. OEIS: A025456, A025418. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_ac899d181597a33f | Erdős Problem #1128 has been DISPROVED (a counterexample is known). Topics: set theory, ramsey theory, hypergraphs. Erdős prize: $50. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_acc09458c248ebed | Erdős Problem #1111 remains OPEN. Topics: graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_acd10050f961f895 | Erdős Problem #595 remains OPEN. Statement: **Erdős Problem 595 ($250)**: Is there an infinite graph $G$ which contains no $K_4$ and is not the union of countably many triangle-free graphs? A problem of Erdős and Hajnal [Er87]. Topics: graph theory, set theory. Erdős prize: $250. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_ad4e1d21eb20e14e | Erdős Problem #65 remains OPEN. Topics: graph theory, cycles. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_ad5ebae8cd245a85 | Erdős Problem #449 has been DISPROVED (a counterexample is known). Topics: number theory, divisors. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_adb1652aa188bae4 | Erdős Problem #1142 remains OPEN. Statement: Are there infinitely many $n > 2$ such that $n - 2^k$ is prime for all $k \geq 1$ with $2^k < n$? The only known such $n$ are $4, 7, 15, 21, 45, 75, 105$ (OEIS [A039669](https://oeis.org/A039669)). Topics: number theory, primes. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A039669. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_adb50d657b7bed82 | Erdős Problem #592 remains OPEN. Statement: Determine which countable ordinals $β$ have the property that, if $α = \omega^β$, then in any red/blue colouring of the edges of $K_α$ there is either a red $K_α$ or a blue $K_3$. Topics: set theory, ramsey theory. Erdős prize: $1000. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_ae08f178d51bb99e | OBLIGATION (Erdos #1056). BANKED: explicit cut-equality certificates verified for every k in 2..14 (interval_product witnesses). OPEN: the problem asks for EVERY k; a uniform construction or proof for all k remains open. | unreviewed | 0.50 | — | — | asserted · 2d |
| vf_ae1baaec0b208389 | Erdős Problem #164 has status 'proved (lean)'. Topics: number theory, primitive sets. Erdős prize: no. Not yet formalized in Lean. OEIS: A137245. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_ae22661fa9878985 | Erdős Problem #1164 has been PROVED (Erdős's conjecture holds). Topics: probability. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_ae6f411b902523c0 | Erdős Problem #118 has been DISPROVED (a counterexample is known). Topics: set theory, ramsey theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_ae7f6a21014b1298 | Erdős Problem #947 has status 'proved (lean)'. Topics: number theory, covering systems. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_aea14e6cfdc43558 | Erdős Problem #730 remains OPEN. Statement: Are there infinitely many pairs of integers $n < m$ such that $\binom{2n}{n}$ and $\binom{2m}{m}$ have the same set of prime divisors? Topics: number theory, binomial coefficients, base representations. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A129515. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_aea1bf6492a81658 | Erdős Problem #265 remains OPEN. Topics: irrationality. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_af5194c239a47256 | Erdős Problem #586 has been DISPROVED (a counterexample is known). Topics: number theory, covering systems. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_af755c088cf40f8a | Erdős Problem #388 remains OPEN. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_af803c3c383cec3d | Erdős Problem #567 remains OPEN. Topics: graph theory, ramsey theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_af9a340f76a26927 | Erdős Problem #108 remains OPEN. Statement: For every r ≥ 4 and k ≥ 2 is there some finite f(k,r) such that every graph of chromatic number ≥ f(k,r) contains a subgraph of girth ≥ r and chromatic number ≥ k? Topics: graph theory, chromatic number, cycles. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_aff975922c8e0373 | Erdős Problem #197 remains OPEN. Statement: Can $\mathbb{N}$ be partitioned into two sets, each of which can be permuted to avoid monotone 3-term arithmetic progressions? Topics: arithmetic progressions. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_b02751141ee46bce | Erdős Problem #1056 remains OPEN. Statement: Let $k ≥ 2$. Does there exist a prime $p$ and consecutive intervals $I_0,\dots,I_k$ such that $\prod\limits_{n{\in}I_i}n \equiv 1 \mod n$ for all $1 \le i \le k$? Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A060427. | unreviewed | 0.99 | — | — | noted · 2d |
| vf_b0291533d8d4136c | Erdős Problem #305 has been PROVED (Erdős's conjecture holds). Topics: number theory, unit fractions. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_b0299898641814e4 | Erdős Problem #1042 has been PROVED (Erdős's conjecture holds). Topics: analysis. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_b06fd0ae66fe8870 | Erdős Problem #358 has been PROVED (Erdős's conjecture holds). Topics: number theory, additive basis, primes. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_b07a88139819313b | Erdős Problem #612 remains OPEN. Topics: graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_b08d9b0b15834934 | Erdős Problem #426 has status 'disproved (lean)'. Topics: graph theory. Erdős prize: $25. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_b0e552f151b4b258 | Erdős Problem #1037 has status 'disproved (lean)'. Topics: graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_b0f3acbe2c674497 | Erdos-Straus conjecture (1948, open): for every integer n >= 2, the equation 4/n = 1/x + 1/y + 1/z has a solution in positive integers x, y, z. Verified computationally for n up to 10^17. | unreviewed | 0.50 | — | — | asserted · 13d |
| vf_b10508e47dce329c | Erdős Problem #836 remains OPEN. Topics: graph theory, hypergraphs, chromatic number. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_b10c1dd412cf6e52 | Erdős Problem #1143 remains OPEN. Topics: number theory, primes. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_b14fb10ae48644ad | Erdős Problem #230 has been DISPROVED (a counterexample is known). Topics: analysis, polynomials. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_b25ddb00c41d0d5a | Erdős Problem #222 remains OPEN. Topics: number theory, squares. Erdős prize: no. Not yet formalized in Lean. OEIS: A256435. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_b26f88e6e2449a7f | Erdős Problem #629 remains OPEN. Topics: graph theory, chromatic number. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_b2b31285fea65ea1 | Erdős Problem #483 remains OPEN. Topics: number theory, additive combinatorics, ramsey theory. Erdős prize: no. Not yet formalized in Lean. OEIS: A030126. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_b2be5ad20671687c | Erdős Problem #965 has been DISPROVED (a counterexample is known). Statement: Erdős asks in [Er75b] if for every 2-coloring of ℝ, there is an uncountable set $A ⊆ ℝ$ such that all sums $a + b$ for $a, b ∈ A, a ≠ b$ have the same colour. In [Ko16] Péter Komjáth constructed a counterexample. The same result was proven independently in [SWCol] by Sokoup and Weiss. Topics: ramsey theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_b2c9adf370bbc6a8 | Erdős Problem #96 remains OPEN. Statement: If $n$ points in $\mathbb{R}^2$ form a convex polygon then there are $O(n)$ many pairs which are distance $1$ apart. Topics: geometry, distances, convex. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_b30b214d80366c5a | Erdős Problem #529 remains OPEN. Topics: geometry, probability. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_b3659a400a56c8ad | Erdős Problem #209 has been DISPROVED (a counterexample is known). Topics: geometry. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_b3764125348b0dbb | Erdős Problem #442 has been DISPROVED (a counterexample is known). Statement: Let $\operatorname{Log} x := \max\{\log x, 1\}$, $\operatorname{Log}_2x = \operatorname{Log} (\operatorname{Log} x)$, and $\operatorname{Log}_3x = \operatorname{Log}(\operatorname{Log}(\operatorname{Log} x)).$ Is it true that if $A\subseteq\mathbb{N}$ is such that $$ \frac{1}{\operatorname{Log}_2 x} \sum_{n\in A: n\leq x} \frac{1}{n}\to\infty $$ then $$ \left(\sum_{n\in A: n\leq x} \frac{1}{n}\right)^2 \sum_{n, m \in A: n < m \leq x} \frac{1}{\operatorname{lcm}(n, m)}\to\infty $$ as $x\to\infty$? Tao [Ta24b] has shown this is false. [Ta24b] Tao, T., _Dense sets of natural numbers with unusually large least common multiples_. arXiv:2407.04226 (2024). Note: the informal and formal statements follow the solution paper https://arxiv.org/pdf/2407.04226 Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_b38a1cfc9adb458f | Erdős Problem #870 remains OPEN. Topics: number theory, additive basis. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_b3b3b5863382d573 | Erdős Problem #387 remains OPEN. Statement: Is there an absolute constant `c > 0` such that, for all `1 ≤ k < n`, the binomial coefficient `n.choose k` has a divisor in `(cn, n]`? Topics: number theory, binomial coefficients. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_b3f75bb1414011bc | Erdős Problem #94 has status 'proved (lean)'. Topics: geometry, convex, distances. Erdős prize: £25. Not yet formalized in Lean. OEIS: A387858. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_b400cae47ff6e159 | Erdős Problem #1163 remains OPEN. Topics: group theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_b44980a7ac2cbf73 | Erdős Problem #890 remains OPEN. Topics: number theory, primes. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_b4569249d794aa1c | Erdős Problem #214 has status 'proved (lean)'. Topics: geometry, distances. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_b48fa7c8511b16c6 | Erdős Problem #684 remains OPEN. Topics: number theory, primes, binomial coefficients. Erdős prize: no. Not yet formalized in Lean. OEIS: A392019, possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_b4a1be219a661b61 | Erdős Problem #485 has been PROVED (Erdős's conjecture holds). Topics: analysis, polynomials. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_b4d4063bd2922457 | Erdős Problem #231 has status 'disproved (lean)'. Topics: combinatorics. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_b4ecf5ea9e1f317b | Erdős Problem #26: machine-found Lean proof published by AlphaProof Nexus (DeepMind, arXiv 2605.22763, May 2026) (Tenenbaum variant — the formalized statement is a variant, not necessarily the full original problem). Independently re-verified locally 2026-06-10: full lake build of google-deepmind/alphaproof-nexus-results@0647711a7118 under their pinned toolchain leanprover/lean4:v4.27.0 succeeded (8062 jobs); static scan clean (no sorry, no native_decide, no custom axioms). Artifacts: erdos_26.variants.tenenbaum.lean sha256:5c48abbba23217e2. AI involvement: machine-generated proof, machine-checked (Lean kernel is the referee); statement faithfulness NOT yet independently attested — see paper section 4 for DeepMind's own expert validation. | unreviewed | 0.90 | — | — | attested · 2d |
| vf_b4fb5aff0d073783 | Erdős Problem #835 has status 'verifiable'. Statement: Does there exist a $k>2$ such that the $k$-sized subsets of {1,...,2k} can be coloured with $k+1$ colours such that for every $A\subset \{1,\ldots,2k\}$ with $\lvert A\rvert=k+1$ all $k+1$ colours appear among the $k$-sized subsets of $A$? Topics: graph theory, hypergraphs. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_b5251963c139582d | Erdős Problem #1192 remains OPEN. Topics: additive combinatorics, additive basis. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_b53818ef62d3672f | Erdős Problem #699 has status 'falsifiable'. Statement: **Erdős Problem 699.** Is it true that for every $1 \le i < j \le n / 2$ there exists a prime $p \ge i$ with $p \mid \gcd\big(\binom{n}{i}, \binom{n}{j}\big)$? Topics: number theory, binomial coefficients. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_b5add23a37a77787 | Erdős Problem #1099 has been PROVED (Erdős's conjecture holds). Topics: number theory, divisors. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_b5ce323db8880fb8 | Erdős Problem #448 has been DISPROVED (a counterexample is known). Topics: number theory, divisors. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_b5f00f8cce5db379 | Erdős Problem #62 remains OPEN. Topics: graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_b64a19a97ddc783d | Erdős Problem #688 remains OPEN. Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_b66b7c5d84d7554e | Erdős Problem #142 remains OPEN. Statement: Prove an asymptotic formula for $r_k(N)$, the largest possible size of a subset of $\{1, \dots, N\}$ that does not contain any non-trivial $k$-term arithmetic progression. Topics: additive combinatorics, arithmetic progressions. Erdős prize: $10000. Statement is machine-verified in Lean (formal-conjectures). OEIS: A003002, A003003, A003004, A003005. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_b691c54cbf309acd | Erdős Problem #189 has status 'disproved (lean)'. Statement: If $\mathbb{R}^2$ is finitely coloured then must there exist some colour class which contains the vertices of a rectangle of every area? Graham, "On Partitions of 𝔼ⁿ", Journal of Combinatorial Theory, Series A 28, 89-91 (1980). (See "Concluding Remarks" on page 96.) Solved (with answer `False`, as formalised below) in: Vjekoslav Kovač, "Coloring and density theorems for configurations of a given volume", 2023 https://arxiv.org/abs/2309.09973 In fact, Kovač's colouring is even Jordan measurable (the topological boundary of each monochromatic region is Lebesgue measurable and has measure zero). This was formalized in Lean by Alexeev and Kovac using Aristotle. Topics: geometry, ramsey theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_b6a5c9b4a08e7b06 | Erdős Problem #557 remains OPEN. Topics: graph theory, ramsey theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_b7182fdb640c48d0 | Erdős Problem #1100 remains OPEN. Topics: number theory, divisors. Erdős prize: no. Not yet formalized in Lean. OEIS: A325864, possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_b74f232c0cea13d5 | Erdős Problem #975 remains OPEN. Statement: For an irreducible polynomial $f \in \mathbb{Z}[x]$ with $f(n) \ge 1$ for sufficiently large $n$, does there exists a constant $c = c(f) > 0$ such that $\sum_{n \le x} \tau(f(n)) \approx c \cdot x \log x$? Note that it is unclear whether the polynomial should have integer coefficients or merely be integer-valued. We assume the former. Topics: number theory, divisors. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A147807, possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_b7642fe4744b032c | Erdős Problem #61 remains OPEN. Statement: The Erdős–Hajnal Conjecture states that there is a constant $c(H) > 0$ for each $H$ such that we can take $f(n) = n^{c(H)}$ in the above formulation. Topics: graph theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_b7647e786ea357c1 | Erdős Problem #329 remains OPEN. Statement: **Erdős Problem 329.** Let `A ⊆ ℕ` be a Sidon set. How large can `lim sup_{N → ∞} |A ∩ {1,…,N}| / N^{1/2}` be? Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_b78593f4982e7382 | Erdős Problem #226 has status 'proved (lean)'. Topics: analysis. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_b7c74f9d3cf0a47c | Erdős Problem #1165 is SOLVED. Topics: probability. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_b8cfc4f93749e3b5 | Erdős Problem #332 remains OPEN. Statement: Let $A\subseteq \mathbb{N}$ and $D(A)$ be the set of those numbers which occur infinitely often as $a_1 - a_2$ with $a_1, a_2\in A$. What conditions on $A$ are sufficient to ensure $D(A)$ has bounded gaps? This is formalised here using the `answer(sorry)` mechanism. In order to solve this problem one has to provide what the sufficient conditions are, and proof that they imply the desired condition. If the condition is a solution to the problem is up to human judgement. Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_b9403c78ff5304fb | Erdős Problem #1135 remains OPEN. Statement: The Collatz conjecture states that for any positive integer $n$, there exists a natural number $m$ such that the $m$-th term of the sequence is 1. Topics: number theory. Erdős prize: $500. Statement is machine-verified in Lean (formal-conjectures). OEIS: A006370, A008908. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_b98c06a783a1e2ec | Erdős Problem #907 has status 'proved (lean)'. Topics: analysis. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_b9e7b2d1475382f3 | Erdős Problem #1080 has status 'disproved (lean)'. Statement: Let $G$ be a bipartite graph on $n$ vertices such that one part has $\lfloor n^{2/3}\rfloor$ vertices. Is there a constant $c>0$ such that if $G$ has at least $cn$ edges then $G$ must contain a $C_6$? The answer is no, as shown by De Caen and Székely [DeSz92], who in fact show a stronger result. Let $f(n,m)$ be the maximum number of edges of a bipartite graph between $n$ and $m$ vertices which does not contain either a $C_4$ or $C_6$. A positive answer to this question would then imply $f(n,\lfloor n^{2/3}\rfloor)\ll n$. De Caen and Székely prove $n^{10/9}\gg f(n,\lfloor n^{2/3}\rfloor) \gg n^{58/57+o(1)}$ for $m\sim n^{2/3}$. They also prove more generally that, for $n^{1/2}\leq m\leq n$, $f(n,m) \ll (nm)^{2/3},$ which was also proved by Faudree and Simonovits. This was formalized in Lean by Alexeev using Aristotle. Topics: graph theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_b9f60ffd2d090057 | Erdős Problem #101 remains OPEN. Statement: Given $n$ points in $\mathbb{R}^2$, no five of which are on a line, the number of lines containing four points is $o(n^2)$. Topics: geometry. Erdős prize: $100. Statement is machine-verified in Lean (formal-conjectures). OEIS: A006065, possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_ba50ac1f1f60aa27 | OBLIGATION (Erdos #684). BANKED: f(M_K-1) > K verified for K=3..12 via Kummer no-carry (effective, subsequential lower bound). OPEN: promote the subsequential bound to the full claim for all n. | unreviewed | 0.50 | — | — | asserted · 2d |
| vf_ba7fb8ad4e8065ab | Erdős Problem #151 remains OPEN. Topics: graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_baed16b00dbce3b6 | Erdős Problem #147 has been DISPROVED (a counterexample is known). Topics: graph theory, turan number. Erdős prize: $500. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_bb06a4c06188a214 | Erdos unit distance problem (1946, open): the maximum number of unit-distance pairs among n points in the plane is at most O(n^(4/3)) (Spencer-Szemeredi-Trotter 1984) and at least Omega(n^(1 + c / log log n)) (Erdos lattice construction); the truth between these is open. | unreviewed | 0.85 | — | — | asserted · 13d |
| vf_bb15794cac47bb4b | Erdős Problem #433 has status 'proved (lean)'. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_bb1d492f0d8c40e1 | Erdős Problem #1166 has been PROVED (Erdős's conjecture holds). Topics: probability. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_bb313b278255c955 | Erdős Problem #1095 remains OPEN. Topics: number theory, binomial coefficients. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A003458. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_bb7f8628ee14154c | Erdős Problem #311 remains OPEN. Topics: number theory, unit fractions. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_bbc8727d595497b8 | Erdős Problem #194 has status 'disproved (lean)'. Statement: Let $k\geq 3$. Must any ordering of $\mathbb{R}$ contain a monotone $k$-term arithmetic progression, that is, some $x_1 <\cdots < x_k$ which forms an increasing or decreasing $k$-term arithmetic progression? The answer is no, even for $k=3$, as shown by Ardal, Brown, and Jungić [ABJ11]. - Topics: arithmetic progressions. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_bbfad3d6c6a62633 | Erdős Problem #407 has been PROVED (Erdős's conjecture holds). Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible, A387688. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_bc0390dcefc5d105 | Erdős Problem #262 is SOLVED. Topics: irrationality. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_bc44a0bd1dc274b4 | Erdős Problem #912 remains OPEN. Statement: Prove that there exists some $c>0$ such that $$h(n) \sim c \left(\frac{n}{\log n}\right)^{1/2}$$ as $n\to \infty$. Topics: number theory, factorials. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A071626. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_bc60ced0147c0c61 | Erdős Problem #859 remains OPEN. Statement: The density of the divisor sum set is asymptotically equivalent to $c_1 / \log(t)^{c_2}$. Topics: number theory, divisors. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_bcc33fa5fd364517 | Erdős Problem #294 has been PROVED (Erdős's conjecture holds). Topics: number theory, unit fractions. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_bccdbb195ab8189d | Erdős Problem #608 has been DISPROVED (a counterexample is known). Topics: graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_bd2103dfb27fa3ca | Erdős Problem #887 remains OPEN. Topics: number theory, divisors. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_bd6b95f7b6975251 | Erdős Problem #161 remains OPEN. Topics: combinatorics, ramsey theory, discrepancy. Erdős prize: $500. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_bd6f63049d1cb1f2 | Erdős Problem #313 remains OPEN. Statement: Are there infinitely many pairs `(m, P)` where `m ≥ 2` is an integer and `P` is a set of distinct primes such that the following equation holds: $\sum_{p \in P} \frac{1}{p} = 1 - \frac{1}{m}$? Topics: number theory, unit fractions. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A054377. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_bd78abefd7a1b770 | Erdős Problem #102 remains OPEN. Topics: geometry. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_bd8bfb7b82fe52a0 | Erdős Problem #953 remains OPEN. Topics: geometry, distances. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_bd97c81be984423e | Erdos sumset conjecture (1976 conjecture, solved 2019 by Moreira-Richter-Robertson): every set of natural numbers with positive upper density contains a sumset B + C where B and C are infinite. | unreviewed | 0.95 | — | — | asserted · 13d |
| vf_bd9fb8cd53ce6b3b | Erdős Problem #1137 remains OPEN. Statement: Let $d_n=p_{n+1}-p_n$, where $p_n$ denotes the $n$th prime. Is it true that $$\frac{\max_{n < x}d_{n}d_{n-1}}{(\max_{n < x}d_n)^2}\to 0$$ as $x\to \infty$? Topics: number theory, primes. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A083550, A005250. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_bdf57bd681a43ab9 | Erdős Problem #675 remains OPEN. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_bf185a960d005806 | Erdős Problem #263 remains OPEN. Topics: irrationality. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_bf2be6a3d0b20a34 | Erdős Problem #1077 has been DISPROVED (a counterexample is known). Statement: We call a graph $D$-balanced (or $D$-almost-regular) if the maximum degree is at most $D$ times the minimum degree. Let $ε, α > 0$ and $D$ and $n$ be sufficiently large. If $G$ is a graph on $n$ vertices with at least $n^{1+α}$ edges, then must $G$ contain a $D$-balanced subgraph on $m > n^{1-α}$ vertices with at least $εm^{1+α}$ edges? Topics: graph theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_bf3add1ff363bf71 | Erdős Problem #881 remains OPEN. Statement: Let `A ⊂ ℕ` be an additive basis of order `k` which is minimal in the sense that if `B ⊂ A` is any infinite set, then `A \ B` is not a basis of order `k`. Must there exist an infinite `B ⊂ A` such that `A \ B` is an additive basis of order `k + 1`? Topics: number theory, additive basis. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_bf3c6c0ad115778e | Erdős Problem #1188 remains OPEN. Topics: number theory, covering systems. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_bfe1c6b2feffeccf | Erdős Problem #819 remains OPEN. Topics: additive combinatorics. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_bffd733e1ce9875c | Erdős Problem #997 has status 'proved (lean)'. Statement: Is it true that, for every $\alpha$, the sequence $\{ \alpha p_n\}$ is not well-distributed, if $p_n$ is the sequence of primes? The answer is yes, by [APSSV26, Section 4]; a Lean formalisation is available in [Mo26]. Topics: analysis, discrepancy, primes. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_c0263b896779ea89 | Erdős Problem #236 remains OPEN. Statement: Let $f(n)$ count the number of solutions to $n=p+2^k$ for prime $p$ and $k\geq 0$. Show that $f(n)=o(\log n)$. Topics: number theory, primes. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A039669, A109925. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_c07bc536b1dc7d7d | Erdős Problem #877 has been PROVED (Erdős's conjecture holds). Topics: additive combinatorics. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_c07d7afea4c1b44a | Erdős Problem #538 remains OPEN. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_c08b2d94ba7f6640 | Erdős Problem #248 has been PROVED (Erdős's conjecture holds). Statement: Are there infinitely many $n$ such that $\omega(n + k) \ll k$ for all $k \geq 1$? Here $\omega(n)$ is the number of distinct prime divisors of $n$. Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_c0e313f1d98afcf3 | Erdős Problem #658 has status 'proved (lean)'. Topics: additive combinatorics. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_c0e3df7a3e7e6cf7 | Erdős Problem #531 remains OPEN. Topics: number theory, ramsey theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_c132496694fea13c | Erdős Problem #1014 has status 'proved (lean)'. Topics: graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_c1461f65ebe68b5b | Erdős Problem #188 remains OPEN. Statement: What is the smallest $k$ such that $\mathbb{R}^2$ can be red/blue coloured with no pair of red points unit distance apart, and no $k$-term arithmetic progression of blue points with distance 1? Topics: geometry, ramsey theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_c14945ee44b33ce6 | Erdős Problem #1182 remains OPEN. Topics: graph theory, ramsey theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_c15f0626f8a26a96 | Erdős Problem #1167 remains OPEN. Statement: **Erdős Problem 1167.** Let $r \geq 2$ be finite and $\lambda$ be an infinite cardinal. Let $\kappa_\alpha$ be cardinals for all $\alpha < \gamma$. Is it true that $$2^\lambda \to (\kappa_\alpha + 1)_{\alpha < \gamma}^{r+1}$$ implies $$\lambda \to (\kappa_\alpha)_{\alpha < \gamma}^r?$$ Here $+$ means cardinal addition, so that $\kappa_\alpha + 1 = \kappa_\alpha$ if $\kappa_\alpha$ is infinite. A problem of Erdős, Hajnal, and Rado. Topics: set theory, probability. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_c18133423f06ef87 | Erdős Problem #229 has status 'proved (lean)'. Statement: Let $(S_n)_{n \ge 1}$ be a sequence of sets of complex numbers, none of which have a finite limit point. Does there exist an entire transcendental function $f(z)$ such that, for all $n \ge 1$, there exists some $k_n \ge 0$ such that $f^{(k_n)}(z) = 0$ for all $z \in S_n$. This is Problem 2.30 in [Ha74], where it is attributed to Erdős. Solved in the affirmative by Barth and Schneider [BaSc72]. This was formalized in Lean by Alexeev using Aristotle. Topics: analysis, iterated functions. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_c186493ccd7d1d7b | Erdős Problem #967 has status 'disproved (lean)'. Topics: number theory, analysis. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_c28dd93882016f42 | Erdős Problem #247 remains OPEN. Statement: Let $n_1 < n_2 < \cdots$ be a sequence of integers such that $$ \limsup \frac{n_k}{k} = \infty. $$ Is $$ \sum_{k=1}^{\infty} \frac{1}{2^{n_k}} $$ transcendental? Topics: number theory, irrationality. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_c2c39e4d50e9d210 | Erdős Problem #949 remains OPEN. Statement: Let $S \subseteq \mathbb{R}$ be a set containing no solutions to $a + b = c$. Must there be a set $A \subseteq \mathbb{R} \setminus S$ of cardinality continuum such that $A + A \subseteq \mathbb{R}\setminus S$? Topics: ramsey theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_c339c21f66014a83 | Erdős Problem #510 remains OPEN. Statement: **Chowla's cosine problem** If $A\subset \mathbb{N}$ is a finite set of positive integers of size $N > 0$ then is there some absolute constant $c>0$ and $\theta$ such that $$\sum_{n\in A}\cos(n\theta) < -cN^{1/2}?$$ Topics: analysis. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_c349ba0ce856e4fd | Erdős Problem #327 remains OPEN. Topics: number theory, unit fractions. Erdős prize: no. Not yet formalized in Lean. OEIS: A384927. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_c385b2b2cc887221 | Erdős Problem #652 has been PROVED (Erdős's conjecture holds). Topics: geometry, distances. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_c38a163c3b5a12d7 | Erdős Problem #958 has status 'disproved (lean)'. Topics: distances, geometry. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_c3a16d0e481ef01d | Erdős Problem #537 has status 'disproved (lean)'. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_c3ba9f8beb2b7d3f | Erdős Problem #987 has been PROVED (Erdős's conjecture holds). Topics: analysis, discrepancy. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_c4d7a3458c698b46 | Erdős Problem #814 has been PROVED (Erdős's conjecture holds). Topics: graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_c56289eee81487c2 | Erdős Problem #540 has status 'proved (lean)'. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: A034463. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_c58b14fac201766e | Erdős Problem #979 remains OPEN. Statement: Let $k ≥ 2$, and let $f_k(n)$ count the number of solutions to $n = p_1^k + \dots + p_k^k$, where the $p_i$ are prime numbers. Is it true that $\limsup f_k(n) = \infty$? Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A385316, possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_c59eb5330b394800 | Erdős Problem #703 has been PROVED (Erdős's conjecture holds). Topics: combinatorics. Erdős prize: $250. Not yet formalized in Lean. OEIS: A390645. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_c629c4f97309ff2c | Erdős Problem #72 has been PROVED (Erdős's conjecture holds). Topics: graph theory, cycles. Erdős prize: $100. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_c74d6e653237ce4a | Erdős Problem #1098 has status 'proved (lean)'. Topics: group theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_c75c23c904515038 | Erdos conjecture on arithmetic progressions (1936, open in general; Green-Tao 2008 resolves the prime case): every set of positive integers whose reciprocal sum diverges contains arbitrarily long arithmetic progressions. | unreviewed | 0.70 | — | — | asserted · 13d |
| vf_c773bca7c1b3fde3 | Erdős Problem #128 has status 'falsifiable'. Statement: Let G be a graph with n vertices such that every subgraph on ≥ $n/2$ vertices has more than $n^2/50$ edges. Must G contain a triangle? Topics: graph theory. Erdős prize: $250. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_c778167eac056216 | Erdős Problem #1146 remains OPEN. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_c7f890d876accf7d | Erdős Problem #1082 has status 'falsifiable'. Topics: geometry, distances. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_c81cf48c54f8aab2 | Erdős Problem #919 remains OPEN. Topics: graph theory, chromatic number. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_c882d79845a4e92d | Erdős Problem #342 remains OPEN. Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A002858. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_c89f4d7a1f57556e | Erdős Problem #43 has been DISPROVED (a counterexample is known). Topics: number theory, sidon sets, additive combinatorics. Erdős prize: $100. Statement is machine-verified in Lean (formal-conjectures). OEIS: A143824, A227590, A003022, possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_c8ce0edef4b9108f | Erdős Problem #354 remains OPEN. Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_c8cecdd3c65fd6cd | Erdős Problem #76 has been PROVED (Erdős's conjecture holds). Topics: graph theory, ramsey theory. Erdős prize: no. Not yet formalized in Lean. OEIS: A060407. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_ca077d3d24c68bc0 | Erdős Problem #777 is SOLVED. Topics: graph theory, combinatorics. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_ca262e3905233c76 | Erdős Problem #1032 remains OPEN. Topics: graph theory, chromatic number. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_ca3bda43e104c7a3 | Erdős Problem #521 remains OPEN. Topics: analysis, polynomials, probability. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_ca9e5579aaa68cb1 | Erdős Problem #208 remains OPEN. Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A005117, A076259. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_caaa525f7259eff1 | Erdős Problem #12: machine-found Lean proof published by AlphaProof Nexus (DeepMind, arXiv 2605.22763, May 2026). Independently re-verified locally 2026-06-10: full lake build of google-deepmind/alphaproof-nexus-results@0647711a7118 under their pinned toolchain leanprover/lean4:v4.27.0 succeeded (8062 jobs); static scan clean (no sorry, no native_decide, no custom axioms). Artifacts: erdos_12.parts.i.lean sha256:c42238294d8d2d88; erdos_12.parts.ii.lean sha256:f155135c1e845cb3. AI involvement: machine-generated proof, machine-checked (Lean kernel is the referee); statement faithfulness NOT yet independently attested — see paper section 4 for DeepMind's own expert validation. | unreviewed | 0.90 | — | — | attested · 2d |
| vf_cab7d323420e1e34 | Erdős Problem #59 has been DISPROVED (a counterexample is known). Topics: graph theory, turan number. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_caef88f0bda6a85e | Erdős Problem #1138 has status 'disproved (lean)'. Topics: number theory, primes. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_cb032234eac3ec43 | Erdős Problem #788 remains OPEN. Topics: additive combinatorics. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_cb0cf1117be8c9c0 | Erdős Problem #1105 has been PROVED (Erdős's conjecture holds). Topics: graph theory, ramsey theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_cb4c6d98c517c621 | Erdős Problem #825 has been PROVED (Erdős's conjecture holds). Statement: Is there an absolute constant $C > 0$ such that every integer $n$ with $\sigma(n) > Cn$ is the distinct sum of proper divisors of $n$? This has been solved in the affirmative by Larsen - in fact, for any $\epsilon>0$ there exists $L$ such that if $n$ has only prime divisors $>L$ and $\sigma(n)>(2+\epsilon)n$ then $n$ is the distinct sum of proper divisors of $n$. Topics: number theory. Erdős prize: $25. Statement is machine-verified in Lean (formal-conjectures). OEIS: A006037, A330244. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_cb73ee70dd3761f9 | Erdős Problem #667 remains OPEN. Topics: graph theory, ramsey theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_cba5e579ff0f16ee | Erdős Problem #385 remains OPEN. Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A322292. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_cc1c4137f01a1b64 | Erdős Problem #296 has status 'proved (lean)'. Topics: number theory, unit fractions. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_cc4742f09a535c49 | Erdős Problem #1117 remains OPEN. Topics: analysis. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_cc60a04d20ddaf6b | Erdős Problem #619 remains OPEN. Topics: graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_cc8d4c30bce54064 | Erdős Problem #840 remains OPEN. Topics: additive combinatorics, sidon sets. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_cc965564ae35491c | Erdős Problem #502 has status 'solved (lean)'. Topics: geometry, distances. Erdős prize: no. Not yet formalized in Lean. OEIS: A027627. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_ccc7665ae24fbc47 | Erdős Problem #500 remains OPEN. Topics: graph theory, hypergraphs, turan number. Erdős prize: $500. Not yet formalized in Lean. OEIS: A140462. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_cce0267cb8eca0a1 | Erdős Problem #12 remains OPEN. Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_cce1010ef447f6b8 | Erdős Problem #663 remains OPEN. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: A391668. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_cd04e79af4515c3b | Erdős Problem #149 remains OPEN. Topics: graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_cd209ae8831333b4 | Erdős Problem #986 remains OPEN. Topics: graph theory, ramsey theory. Erdős prize: no. Not yet formalized in Lean. OEIS: A000791, A059442. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_cd46c7499a157984 | Erdős Problem #469 remains OPEN. Statement: Let $A$ be the set of all $n$ such that $n = d_1 + ⋯ + d_k$ with $d_i$ distinct proper divisors of $n$, but this is not true for any $m ∣ n$ with $m < n$. Does: $$ \sum_{n ∈ A} \frac 1 n $$ converge? Topics: number theory, divisors. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A006036, A119425, possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_cd55f87cd913de3f | Erdős Problem #830 remains OPEN. Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A259180. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_cd577c61f64a83c1 | Erdős Problem #268 has status 'proved (lean)'. Statement: Let `X` be the set of points in `Fin d → ℝ` of the shape `fun i : Fin d => ∑' n : A, (1 : ℝ) / (n + i)` for some infinite subset `A ⊆ ℕ` such that `1 / n` is summable over `A`. `X` has nonempty interior. This is proved in [KoTa24]. - Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_cd5b07b68b45543c | Erdős Problem #915 is SOLVED. Topics: graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_cd5fe218ed92cc31 | OBLIGATION (Erdos #366). BANKED: the unconditional Mordell-curve reduction + Pell correction + the two analytic walls verified. OPEN: the analytic walls block an unconditional bound; closing them is open. | unreviewed | 0.50 | — | — | asserted · 2d |
| vf_cd90f1defdd5e12b | Erdős Problem #1085 remains OPEN. Topics: geometry, distances. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A186705, possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_cdc7151fc32e0218 | Erdős Problem #6 has been PROVED (Erdős's conjecture holds). Statement: There are infinitely many $n$ such that $d_n < d_{n+1} < d_{n+2}$, where $d$ denotes the prime gap function. Topics: number theory, primes. Erdős prize: $100. Statement is machine-verified in Lean (formal-conjectures). OEIS: A335277. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_ce2c32196727e21e | Erdős Problem #1162 remains OPEN. Topics: group theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_ce31d7f19ec83d61 | Erdős Problem #1052 remains OPEN. Statement: Are there only finitely many unitary perfect numbers? Topics: number theory. Erdős prize: $10. Statement is machine-verified in Lean (formal-conjectures). OEIS: A002827. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_ce540b4c4213c02a | Erdős Problem #921 has been PROVED (Erdős's conjecture holds). Topics: graph theory, chromatic number, cycles. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_ce5be5192cf77254 | Erdős Problem #910 has been DISPROVED (a counterexample is known). Topics: topology. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_cec6cfa6f9c7052e | Erdős Problem #966 has status 'proved (lean)'. Topics: number theory, additive combinatorics, ramsey theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_cef5900bd7ac7bcc | Erdős Problem #497 has status 'solved (lean)'. Topics: combinatorics. Erdős prize: no. Not yet formalized in Lean. OEIS: A000372. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_cf0673734ee26e43 | Erdős Problem #180 remains OPEN. Topics: graph theory, turan number. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_cf11693b294b8e79 | Erdős Problem #50 remains OPEN. Statement: Let $f$ be the asymptotic distribution function of $\varphi(n)/n$, so that for each $c \in [0,1]$, $f(c)$ is the natural density of $\{n : \varphi(n) < cn\}$. Is it true that there is no $x$ such that the derivative $f'(x)$ exists and is positive? Topics: number theory. Erdős prize: $250. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_cf530db62fe87ae0 | Erdős Problem #635 remains OPEN. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_cf72d61521c4c4f4 | Erdős Problem #711 remains OPEN. Topics: number theory. Erdős prize: ₹1000. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_d029f0e358de5622 | Erdős Problem #842 has been PROVED (Erdős's conjecture holds). Topics: graph theory, chromatic number. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_d07030a921f48680 | Erdős Problem #1185 is SOLVED. Topics: additive combinatorics, arithmetic progressions. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_d0750e30ddf3b801 | Erdős Problem #175 has been PROVED (Erdős's conjecture holds). Topics: number theory, binomial coefficients. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_d081790f0fc855e0 | Erdős Problem #611 remains OPEN. Topics: graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_d0859d0c90f623c8 | Erdős Problem #897 has status 'disproved (lean)'. Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_d0caa966c4117569 | Erdős Problem #1179 has been PROVED (Erdős's conjecture holds). Topics: additive combinatorics, probability. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_d1267a6605407375 | Erdős Problem #587 is SOLVED. Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A372040. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_d13bae6e4e4bf306 | Erdős Problem #1112 remains OPEN. Topics: additive combinatorics. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_d13e235420b43f13 | Erdős Problem #473 has been PROVED (Erdős's conjecture holds). Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: A055265. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_d1f1c6f3b19aaf08 | Erdős Problem #740 remains OPEN. Statement: Let $\mathfrak{m}$ be an infinite cardinal and $G$ be a graph with chromatic number $\mathfrak{m}$. Let $r\geq 1$. Must $G$ contain a subgraph of chromatic number $\mathfrak{m}$ which does not contain any odd cycle of length $\leq r$? Topics: graph theory, chromatic number. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_d1f78c518c342fc0 | Erdős Problem #1087 remains OPEN. Topics: geometry, distances. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_d25ad78d364840bc | Erdős Problem #792 remains OPEN. Topics: additive combinatorics. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_d2a27270867e4632 | Erdős Problem #847 has been DISPROVED (a counterexample is known). Statement: Let $A \subset \mathbb{N}$ be an infinite set for which there exists some $\epsilon > 0$ such that in any subset of $A$ of size $n$ there is a subset of size at least $\epsilon n$ which contains no three-term arithmetic progression. Is it true that $A$ is the union of a finite number of sets which contain no three-term arithmetic progression? A negative answer was given by Reiher, Rödl, and Sales [RRS24], who proved that, for any $0<\mu<1/2$, there exists $A\subseteq \mathbb{N}$ such that every finite colouring of $A$ contains a three-term arithmetic progression, and yet every subset of $A$ of size $n$ contains a subset of size $\geq \mu n$ without a three-term arithmetic progression. Topics: additive combinatorics. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_d2e1cf3758199eb3 | Erdős Problem #184 remains OPEN. Statement: Any graph on $n$ vertices can be decomposed into $O(n)$ many edge-disjoint cycles and edges. Topics: graph theory, cycles. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_d2e1d88d122b4ce9 | Erdős Problem #131 remains OPEN. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: A068063. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_d2ff7983024f73bb | Erdős Problem #38 has status 'proved (lean)'. Statement: Does there exist $B \subset \mathbb{N}$ which is not an additive basis, but is such that for every set $A \subseteq \mathbb{N}$ of Schnirelmann density $\alpha$ and every $N$ there exists $b \in B$ such that $$ \lvert (A \cup (A+b)) \cap \{1, \ldots, N\} \rvert \geq (\alpha + f(\alpha)) N $$ where $f(\alpha) > 0$ for $0 < \alpha < 1$? Note: here Erdős seems to use a slightly weaker notion of an additive basis (see [Er56] at the top of page 135). In particular, for this problem, a set is an additive basis of order $k$ if every natural number can be written as a sum of _at most_ $k$ elements of the set, rather than as a sum of _precisely_ $k$ elements. A positive [solution](https://github.com/spicylemonade/erdos-38) was given by GPT 5.5 Pro (prompted by gebyjaff, cleanup by Liam Price); in fact a sparse random set $B$ has this property, with $f(\alpha)\gg \alpha (1-\alpha)^2$. Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_d3606d7813f44f08 | Erdős Problem #899 has been PROVED (Erdős's conjecture holds). Statement: Let $A\subseteq\mathbb{N}$ be an infinite set such that $|A\cap \{1, ..., N\}| = o(N)$. Is it true that $$ \limsup_{N\to\infty}\frac{|(A - A)\cap \{1, ..., N\}|}{|A \cap \{1, ..., N\}|} = \infty? $$ The answer is yes, proved by Ruzsa [Ru78]. [Ru78] Ruzsa, I. Z., _On the cardinality of {$A+A$}\ and {$A-A$}_. (1978), 933--938. Topics: additive combinatorics. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_d3958ad7bba76181 | Erdős Problem #924 has been PROVED (Erdős's conjecture holds). Topics: graph theory, ramsey theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_d3d947902c6331cb | Erdős Problem #319 remains OPEN. Statement: What is the size of the largest $A\subseteq\{1, \dots, N\}$ such that there is a function $\delta : A \to \{-1, 1\}$ such that $$ \sum_{n\in A} \frac{\delta n}{n} = 0 $$ and $$ \sum_{n\in A'}\frac{\delta n}{n} \neq 0 $$ for all non-empty $A'\subsetneq A$. Topics: number theory, unit fractions. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_d44d02bd8742e344 | Erdős Problem #163 has been PROVED (Erdős's conjecture holds). Topics: graph theory, ramsey theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_d46da9898913e895 | Erdős Problem #1178 remains OPEN. Topics: graph theory, hypergraphs. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_d478a9264bef8eb1 | Erdős Problem #281 has status 'proved (lean)'. Topics: number theory, covering systems. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_d4c343be07684ce7 | Erdős Problem #1204 remains OPEN. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: A008407, A023193, A135311, possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_d535d2c3484cdb57 | Erdős Problem #1125 has status 'proved (lean)'. Topics: analysis. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_d5405dca29541690 | Erdős Problem #1216 has been DISPROVED (a counterexample is known). Topics: graph theory, ramsey theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_d55624726ec25be7 | Erdős Problem #462 remains OPEN. Topics: number theory, primes. Erdős prize: no. Not yet formalized in Lean. OEIS: A032742, possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_d5706b13c19bc9f2 | Erdős Problem #416 remains OPEN. Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A264810. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_d5f52f9e4417a23b | Erdős Problem #1106 remains OPEN. Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A194259, A194260. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_d5f76e0d6438164e | Erdős Problem #574 has been DISPROVED (a counterexample is known). Topics: graph theory, turan number. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_d60a12f70bf04aa8 | Erdos discrepancy problem (1932 conjecture, solved 2015 by Tao): for every sign sequence and every constant C, there exist d, k such that the partial sum sum_{i=1}^k epsilon(id) exceeds C in absolute value. | unreviewed | 0.95 | — | — | asserted · 13d |
| vf_d64ebfc59dad4fec | Erdős Problem #519 has status 'proved (lean)'. Topics: analysis. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_d673ef5dbbdfa74c | Erdős Problem #285 has been PROVED (Erdős's conjecture holds). Statement: Let $f(k)$ be the minimal value of $n_k$ such that there exist $n_1 < n_2 < \dots < n_k$ with $$ 1 = \frac{1}{n_1} + \cdots + \frac{1}{n_k}. $$ Is it true that $$ f(k) = (1 + o(1)) \frac{e}{e - 1} k ? $$ Proved by Martin [Ma00]. [Ma00] Martin, Greg, _Denser Egyptian fractions_. Acta Arith. (2000), 231-260. Topics: number theory, unit fractions. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A030659. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_d6ad604be783e501 | Erdős Problem #689 remains OPEN. Statement: Let `n` be sufficiently large. Is there some choice of congruence class `a_p` for all primes `2 ≤ p ≤ n` such that every integer in `[1,n]` satisfies at least two of the congruences `≡ a_p (mod p)`? Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_d72bce755ab746a2 | Erdős Problem #366 has status 'verifiable'. Statement: Are there any $2$-full $n$ such that $n+1$ is $3$-full? Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A060355. | unreviewed | 0.99 | — | — | noted · 2d |
| vf_d72e9119de22c7fb | Erdős Problem #1145 remains OPEN. Statement: Let $A=\{1\leq a_1 < a_2 < \cdots\}$ and $B=\{1\leq b_1 < b_2 < \cdots\}$ be sets of integers with $a_n/b_n\to 1$. If $A+B$ contains all sufficiently large positive integers then is it true that $\limsup 1_A\ast 1_B(n)=\infty$? A conjecture of Erdős and Sárközy. Topics: additive combinatorics, additive basis. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_d73d02fd5b4d6b80 | Erdős Problem #1024 is SOLVED. Topics: graph theory, hypergraphs. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_d8c5d0202f1da744 | Erdős Problem #156 remains OPEN. Topics: sidon sets. Erdős prize: no. Not yet formalized in Lean. OEIS: A382397. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_d8c8fe489da91f82 | Erdős Problem #599 has been PROVED (Erdős's conjecture holds). Topics: graph theory, set theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_d8e5cf694d32288f | Erdős Problem #1198 has been DISPROVED (a counterexample is known). Topics: additive combinatorics, ramsey theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_d8e9f7fe0cf1ce49 | Erdős Problem #1067 has status 'disproved (lean)'. Statement: Does every graph with chromatic number $\aleph_1$ contain an infinitely connected subgraph with chromatic number $\aleph_1$? Komjáth [Ko13] proved that it is consistent that the answer is no. This was improved by Soukup [So15], who constructed a counterexample using no extra set-theoretical assumptions. A simpler elementary example was given by Bowler and Pitz [BoPi24]. This was formalized in Lean by Alexeev using Aristotle and Aleph Prover. Topics: graph theory, set theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_d993f146c83b73b4 | Erdős Problem #1102 has status 'solved (lean)'. Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_d9d6f37d64bdf3fd | Erdős Problem #438 is SOLVED. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: A363069. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_d9e346b8e73b7626 | Erdős Problem #152 has been PROVED (Erdős's conjecture holds). Statement: Must `lim f n = ∞`? This was proved formally by the DeepMind prover agent [DM26a]. Topics: sidon sets. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_da2a4ba8dac92823 | Erdős Problem #988 is SOLVED. Topics: discrepancy. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_da3cc7a48e736726 | Erdős Problem #292 has been PROVED (Erdős's conjecture holds). Topics: number theory, unit fractions. Erdős prize: no. Not yet formalized in Lean. OEIS: A092671. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_da67ae23bd199852 | Erdős Problem #83 has been PROVED (Erdős's conjecture holds). Topics: combinatorics. Erdős prize: $500. Not yet formalized in Lean. OEIS: A071799, A387635. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_da8be2d26ff3b53f | Erdős Problem #1016 remains OPEN. Topics: graph theory, cycles. Erdős prize: no. Not yet formalized in Lean. OEIS: A105206. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_da8d51a6cae5ec11 | OBLIGATION (Erdos #617). BANKED: K25 balanced-coloring construction known; the K26 finite case is the first open case and reduces to a SAT instance. OPEN: produce the LRAT/RAT certificate for the K26 SAT encoding and re-check it with `vela reproduce` (unsat_cert); the symmetry-breaking step needs RAT, beyond the current RUP checker. | unreviewed | 0.50 | — | — | asserted · 2d |
| vf_dad4a47febaa57f5 | Erdős Problem #1022 has status 'proved (lean)'. Topics: combinatorics, hypergraphs. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_dad9e92801e040dc | Erdős Problem #495 remains OPEN. Statement: Let $\alpha,\beta \in \mathbb{R}$. Is it true that$$\liminf_{n\to \infty} n \| n\alpha \| \| n\beta\| =0$$? This is also known as the Littlewood conjecture. Topics: diophantine approximation, number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_daf1a088f7f2b0d2 | Erdős Problem #345 remains OPEN. Topics: number theory, complete sequences. Erdős prize: no. Not yet formalized in Lean. OEIS: A001661. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_db0c6ad5275044fa | Erdős Problem #911 remains OPEN. Topics: graph theory, ramsey theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_db0d51be882951b8 | Erdős Problem #178 has status 'proved (lean)'. Topics: discrepancy. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_db2333e894658e5a | Erdős Problem #104 remains OPEN. Topics: geometry. Erdős prize: $100. Not yet formalized in Lean. OEIS: A003829. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_db2ec1f8dbb7405b | Erdős Problem #63 has been PROVED (Erdős's conjecture holds). Topics: graph theory, chromatic number, cycles. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_db3a6da3be5970d0 | Erdős Problem #1047 has status 'disproved (lean)'. Topics: analysis. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_db51f8a305cbaaf0 | Erdos-Faber-Lovasz conjecture (1972, solved for sufficiently large n in 2021): the chromatic index of the union of n complete graphs of order n that pairwise share at most one vertex is exactly n. | unreviewed | 0.90 | — | — | asserted · 13d |
| vf_db6cc07678873270 | Erdős Problem #172 remains OPEN. Statement: Is it true that in any finite colouring of $\mathbb{N}$ there exist arbitrarily large finite $A$ such that all sums and products of distinct elements in $A$ are the same colour? Topics: additive combinatorics, ramsey theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_dbb3d410c5780894 | Erdős Problem #1030 remains OPEN. Topics: graph theory, ramsey theory. Erdős prize: no. Not yet formalized in Lean. OEIS: A000791, A059442. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_dc157795c6c0b7df | Erdős Problem #902 remains OPEN. Topics: graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: A362137. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_dc3eef92cf01e066 | Erdős Problem #713 remains OPEN. Topics: graph theory, turan number. Erdős prize: $500. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_dc80bc1e80869b2a | Erdős Problem #95 has been PROVED (Erdős's conjecture holds). Topics: geometry, convex, distances. Erdős prize: $500. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_dcd4edd5fbcc106b | Erdős Problem #1072 remains OPEN. Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A073944, A072937, A154554. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_dce8c38915751145 | Erdős Problem #816 has been PROVED (Erdős's conjecture holds). Topics: graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_dcfa45ce922b501a | Erdős Problem #309 has been DISPROVED (a counterexample is known). Topics: number theory, unit fractions. Erdős prize: no. Not yet formalized in Lean. OEIS: A217693. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_dd07024ad9830b35 | Erdős Problem #293 remains OPEN. Topics: number theory, unit fractions. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_dd0fb4045047b3c2 | Erdős Problem #704 remains OPEN. Topics: graph theory, geometry, chromatic number. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_dd5263e9d8bf8364 | Erdős Problem #493 has status 'proved (lean)'. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_dd8722cf933def36 | Erdős Problem #657 remains OPEN. Topics: geometry, distances. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_ddb9c860c0282084 | Erdős Problem #882 is SOLVED. Topics: number theory, primitive sets. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_ddee7c7742dd062b | Erdős Problem #443 has status 'proved (lean)'. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_ddf9a0caad805397 | Erdős Problem #390 remains OPEN. Statement: Does there exists a constant `c` such that `f n - 2 * n ~ c * (n / log n)`? Topics: number theory, factorials. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A193429. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_de042c9de47e7b8c | Erdős Problem #1160 remains OPEN. Topics: group theory. Erdős prize: no. Not yet formalized in Lean. OEIS: A000001. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_de53431c24b503f8 | Erdős Problem #239 has been PROVED (Erdős's conjecture holds). Statement: Let $f:\mathbb{N}\to \{-1,1\}$ be a multiplicative function. Is it true that $$ \lim_{N\to \infty}\frac{1}{N}\sum_{n\leq N}f(n)$$ always exists? The answer is yes, as proved by Wirsing [Wi67], and generalised by Halász [Ha68]. Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_de670165a5fa2e8d | Erdős Problem #681 remains OPEN. Statement: **Erdős problem 681.** Is it true that for all large $n$ there exists $k$ such that $n + k$ is composite and $p(n+k) > k^2$, where $p(m)$ is the least prime factor of $m$ ? Topics: number theory, primes. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A389680. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_de82cac117220ee9 | Erdős Problem #646 has status 'proved (lean)'. Topics: number theory, factorials. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_de9a430867c11135 | Erdős Problem #686 remains OPEN. Statement: Can every integer $N≥2$ be written as $$N=\frac{\prod_{1\leq i\leq k}(m+i)}{\prod_{1\leq i\leq k}(n+i)}$$ for some $k≥2$ and $m≥n+k$? Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_dea9fb9c355ececc | Erdős Problem #1184 remains OPEN. Topics: number theory, primes. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_deab70866d6c363d | Erdős Problem #716 has been PROVED (Erdős's conjecture holds). Topics: graph theory, hypergraphs. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_deaf2ac437f1ff60 | Erdős Problem #52 remains OPEN. Statement: Let $A$ be a finite set of integers. Is it true that for every $\epsilon>0$ $\max( \lvert A+A\rvert,\lvert AA\rvert)\gg_\epsilon \lvert A\rvert^{2-\epsilon}?$ Topics: number theory, additive combinatorics. Erdős prize: $250. Statement is machine-verified in Lean (formal-conjectures). OEIS: A263996. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_ded2571ab783b63d | Erdős Problem #1071 has status 'proved (lean)'. Topics: geometry. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_ded34e6d69ce9295 | Erdős Problem #4 has been PROVED (Erdős's conjecture holds). Statement: Is it true that, for any $C > 0$, there infinitely many $n$ such that: $$ p_{n + 1} - p_n > C \frac{\log\log n\log\log\log\log n}{(\log\log\log n) ^ 2}\log n $$ Topics: number theory, primes. Erdős prize: $10000. Statement is machine-verified in Lean (formal-conjectures). OEIS: A002386. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_df5b851547e9bcfb | Erdős Problem #863 has been PROVED (Erdős's conjecture holds). Topics: number theory, sidon sets, additive combinatorics. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_df7ea5cd659d9ee3 | Erdős Problem #454 remains OPEN. Statement: Is it true that `limsup (fun n => (f n - 2 * n.nth Prime : ℕ∞)) atTop = ⊤`? Topics: number theory, primes. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A389676, A389677. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_dfa18afccec088bd | Erdős Problem #99 remains OPEN. Statement: For sufficiently large n, is it the case that any set of n points with minimum distance $1$ that minimizes diameter must contain an equilateral triangle of side length 1? Topics: geometry, distances. Erdős prize: $100. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_dfa83c963b198e88 | Erdős Problem #572 remains OPEN. Topics: graph theory, turan number. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_dfc5c3d1545742c5 | Erdős Problem #201 remains OPEN. Topics: additive combinatorics, arithmetic progressions. Erdős prize: no. Not yet formalized in Lean. OEIS: A003002, A003003, A003004, A003005, possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_e004726ecce96ed0 | Erdős Problem #26 has status 'disproved (lean)'. Statement: Let $A\subset\mathbb{N}$ be infinite such that $\sum_{a \in A} \frac{1}{a} = \infty$. Must there exist some $k\geq 1$ such that almost all integers have a divisor of the form $a+k$ for some $a\in A$? This was formalized in Lean by Alexeev using Aristotle. Topics: number theory, divisors. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_e02d21620beae0a1 | Erdős Problem #634 remains OPEN. Topics: geometry. Erdős prize: $25. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_e03590a9131c59a7 | Erdős Problem #289 remains OPEN. Statement: Is it true that, for all sufficiently large $k$, there exists finite intervals $I_1, \dotsc, I_k \subset \mathbb{N}$ with $|I_i| \geq 2$ for $1 \leq i \leq k$ such that $$ 1 = \sum_{i=1}^k \sum_{n \in I_i} \frac{1}{n}. $$ Topics: number theory, unit fractions. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_e096e1775b4a3774 | Erdős Problem #695 remains OPEN. Statement: Let $q_1 < q_2 < \cdots$ be a sequence of primes such that $q_{i + 1} \equiv 1 \pmod{q_i}$. Is it true that $$ \lim_{k \to \infty} q_k^{1/k} = \infty? $$ Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A061092. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_e10aa62ba12b2212 | Erdős Problem #876 remains OPEN. Topics: additive combinatorics. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_e177c073ef12405f | Erdős Problem #302 remains OPEN. Topics: number theory, unit fractions. Erdős prize: no. Not yet formalized in Lean. OEIS: A390395. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_e1813c4a0ed1035d | Erdős Problem #797 has been PROVED (Erdős's conjecture holds). Topics: graph theory, chromatic number. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_e18e5aba75d2fd63 | Erdős Problem #1025 is SOLVED. Topics: combinatorics. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_e194e88434182d37 | Erdős Problem #368 remains OPEN. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: A074399. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_e27e3de8428db7f2 | Erdős Problem #79 has been PROVED (Erdős's conjecture holds). Topics: graph theory, ramsey theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_e336d6e8169251de | Erdős Problem #494 has been PROVED (Erdős's conjecture holds). Topics: analysis, additive combinatorics. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_e362eab19f30e399 | Erdős Problem #739 has status 'not provable'. Topics: graph theory, chromatic number. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_e40e32ac39d01c18 | Erdős Problem #862 has status 'solved (lean)'. Topics: number theory, sidon sets. Erdős prize: no. Not yet formalized in Lean. OEIS: A382395. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_e4703596814f59e4 | Erdős Problem #570 has been PROVED (Erdős's conjecture holds). Topics: graph theory, ramsey theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_e48885d4d317ec44 | Erdős Problem #349 remains OPEN. Statement: For what values of $t,\alpha \in (0,\infty)$ is the sequence $\lfloor t\alpha^n\rfloor$ complete (that is, all sufficiently large integers are the sum of distinct integers of the form $\lfloor t\alpha^n\rfloor$)? Topics: number theory, complete sequences. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_e4dbdf5212750a05 | Erdős Problem #1130 has been PROVED (Erdős's conjecture holds). Topics: analysis, polynomials. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_e4ddb7020db7c34a | Erdős Problem #362 has been PROVED (Erdős's conjecture holds). Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_e50f1046e4e8e6bf | Erdős Problem #742 has status 'decidable'. Topics: graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_e52ecf6f539620cc | Erdős Problem #344 has been PROVED (Erdős's conjecture holds). Topics: number theory, complete sequences. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_e57b2f6fe26bfed2 | Erdős Problem #1139 remains OPEN. Statement: Let $1\leq u_1 < u_2 < \cdots$ be the sequence of integers with at most $2$ prime factors. Is it true that $$\limsup_{k \to \infty} \frac{u_{k+1}-u_k}{\log k}=\infty?$$ Topics: number theory, primes. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_e595861030753fa6 | Erdős Problem #930 remains OPEN. Statement: Is it true that, for every $r$, there is a $k$ such that if $I_1,\ldots,I_r$ are disjoint intervals of consecutive integers, all of length at least $k$, then $$ \prod_{1\leq i\leq r}\prod_{m\in I_i}m $$ is not a perfect power? Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_e59a46bcfdf0d435 | Erdős Problem #393 remains OPEN. Topics: number theory, factorials. Erdős prize: no. Not yet formalized in Lean. OEIS: A388302. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_e59c3703def0ee46 | Erdős Problem #1127 has status 'independent'. Topics: geometry, distances, set theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_e5a829e19b7dd9a8 | Erdős Problem #392 has status 'proved (lean)'. Statement: Let $A(n)$ denote the least value of $t$ such that $$ n! = a_1 \cdots a_t $$ with $a_1 \leq \cdots \leq a_t\leq n^2$. Then $$ A(n) = \frac{n}{2} - \frac{n}{2\log n} + o\left(\frac{n}{\log n}\right). $$ Topics: number theory, factorials. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_e5e19bef5239e1be | Erdős Problem #457 has status 'proved (lean)'. Statement: Is there some $\epsilon > 0$ such that there are infinitely many $n$ where all primes $p \le (2 + \epsilon) \log n$ divide $$ \prod_{1 \le i \le \log n} (n + i)? $$ This was formalized in Lean by Baretto and van Doorn using Aristotle. Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A391668. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_e65bc444dae27dae | Erdős Problem #399 has status 'disproved (lean)'. Statement: Is it true that there are no solutions to `n! = x^k ± y^k` with `x,y,n ∈ ℕ`, `x*y > 1`, and `k > 2`? The answer is no: Jonas Barfield found the counterexample `10! = 48^4 - 36^4` (equivalently, `10! + 36^4 = 48^4`). This is discussed in problem D2 of Guy's collection [Gu04]. This was formalized in Lean by Lu using Codex. Topics: number theory, factorials. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_e693f890fc5a90c7 | Erdős Problem #728 has status 'proved (lean)'. Statement: Let $\varepsilon$ be sufficiently small and $C, C' > 0$. Are there integers $a, b, n$ such that $$a, b > \varepsilon n\quad a!\, b! \mid n!\, (a + b - n)!, $$ and $$C \log n < a + b - n < C' \log n ?$$ Note that the website currently displays a simpler (trivial) version of this problem because $a + b$ isn't assumed to be in the $n + O(\log n)$ regime. Barreto and ChatGPT-5.2 have proved that, for any $0 < C_1 < C_2$, there are infinitely many $a, b, n$ with $b = n/2$, $a = n/2 + O(\log n)$, and $C_1 \log n < a + b - n < C_2 \log n$ such that $a! b! \mid n! (a + b - n)!$ This appears to answer the question in the spirit it was intended. This was formalized in Lean by Alexeev using Aristotle. Topics: number theory, factorials. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_e6a1f3ddf3ac6a39 | Erdős Problem #446 is SOLVED. Topics: number theory, divisors. Erdős prize: no. Not yet formalized in Lean. OEIS: A074738. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_e765efcb2624605c | Erdős Problem #1084 remains OPEN. Topics: geometry, distances. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A045945, possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_e78ce45079841e8a | Erdős Problem #39 remains OPEN. Statement: Is there an infinite Sidon set $A\subset \mathbb{N}$ such that $\lvert A\cap \{1\ldots,N\}\rvert \gg_\epsilon N^{1/2-\epsilon}$ for all $\varepsilon > 0$? Topics: number theory, sidon sets, additive combinatorics. Erdős prize: $500. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_e7d5ce1e93a9c623 | Erdős Problem #20 remains OPEN. Statement: Is it true that $f(n,k) < c_k^n$ for some constant $c_k>0$ and for all $n > 0$? Topics: combinatorics. Erdős prize: $1000. Statement is machine-verified in Lean (formal-conjectures). OEIS: A332077. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_e823623ec8d3d858 | Erdős Problem #337 has status 'disproved (lean)'. Topics: number theory, additive combinatorics, additive basis. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_e854587794a28b73 | Erdős Problem #626 remains OPEN. Topics: graph theory, chromatic number, cycles. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_e8cef3cd32a2919e | Erdős Problem #763 has been DISPROVED (a counterexample is known). Topics: number theory, additive combinatorics. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_e8d9ad1e5e9aed51 | Erdős Problem #932 remains OPEN. Statement: Let $p_k$ denote the $k$th prime. For infinitely many $r$ there are at least two integers $p_r < n < p_{r+1}$ all of whose prime factors are $< p_{r + 1} - p_r$. Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A387864. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_e92304a9bcb5831c | Erdős Problem #655 remains OPEN. Statement: Let $x_1,\ldots,x_n\in \mathbb{R}^2$ be such that no circle whose centre is one of the $x_i$ contains three other points. Are there at least $$(1+c)\frac{n}{2}$$ distinct distances determined between the $x_i$, for some constant $c>0$ and all $n$ sufficiently large? Zach Hunter has observed that taking $n$ points equally spaced on a circle disproves one natural interpretation of this conjecture. Topics: geometry, distances. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_e92c06f6d30fde78 | Erdős Problem #1208 remains OPEN. Topics: geometry, distances. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_e92e3e87707676b4 | Erdős Problem #1116 is SOLVED. Topics: analysis. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_e989a9337c2d241c | Erdős Problem #277 has been PROVED (Erdős's conjecture holds). Statement: Is it true that, for every $c$, there exists an $n$ such that $\sigma(n)>cn$ but there is no covering system whose moduli all divide $n$? This was answered affirmatively by Haight [Ha79]. Topics: number theory, covering systems. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_e98c39e418546862 | Erdős Problem #41 remains OPEN. Statement: Let `A ⊆ ℕ` be an infinite set such that the triple sums `a + b + c` are all distinct for `a, b, c` in `A` (aside from the trivial coincidences). Is it true that `liminf n → ∞ |A ∩ {1, …, N}| / N^(1/3) = 0`? Topics: number theory, sidon sets, additive combinatorics. Erdős prize: $500. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_e9e8b34f2a6a7b1d | Erdos-Ginzburg-Ziv theorem (1961, solved): among any 2n-1 integers, there exist n whose sum is divisible by n. Tight: 2n-2 integers may admit no such subset. | unreviewed | 0.98 | — | — | asserted · 4w |
| vf_ea0daf4b37b7c3d7 | Erdős Problem #939 remains OPEN. Statement: If $r≥4$ then can the sum of $r-2$ coprime $r$-powerful numbers ever be itself $r$-powerful? Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_ea19c60ebb0ea691 | Erdős Problem #143 remains OPEN. Topics: primitive sets. Erdős prize: $500. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_ea4406165bd0495c | Erdős Problem #255 has been PROVED (Erdős's conjecture holds). Topics: discrepancy. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_ea61cd22f878d33d | Erdős Problem #577 has been PROVED (Erdős's conjecture holds). Topics: graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_ead7b9cb8ae62598 | Erdős Problem #696 has status 'solved (lean)'. Topics: number theory, divisors. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_eaed732407f3cc32 | Erdős Problem #103 remains OPEN. Topics: geometry, distances. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_eb741f9becc60879 | OBLIGATION (Erdos #699). BANKED: the central-doubling reduction + CRT obstruction verified; the two arms provably do not meet. OPEN: the gap between the arms is the open obstruction. | unreviewed | 0.50 | — | — | asserted · 2d |
| vf_eb851957b3e6491f | Erdős Problem #275 has status 'proved (lean)'. Statement: If a finite system of $r$ congruences $\{ a_i\pmod{n_i} : 1\leq i\leq r\}$ (the $n_i$ are not necessarily distinct) covers $2^r$ consecutive integers then it covers all integers. This is best possible as the system $2^{i-1}\pmod{2^i}$ shows. This was proved independently by Selfridge and Crittenden and Vanden Eynden [CrVE70]. This was formalized in Lean by Alexeev using Aristotle. Topics: number theory, covering systems. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_eb9901d14a1b0b52 | Erdős Problem #893 remains OPEN. Statement: Does the limit $\lim_{n\to\infty} \frac{f(2n)}{f(n)}$ tend to infinity? (Other finite limits have been ruled out by [KoLu25], see below) Topics: number theory, divisors. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A046801, possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_eb9bd62c1c30e042 | Erdős Problem #146 remains OPEN. Topics: graph theory, turan number. Erdős prize: $500. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_ebe62e7e343f953c | Erdős Problem #190 remains OPEN. Topics: additive combinatorics, arithmetic progressions. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_ec4253e61bfa4884 | Erdős Problem #35 has been PROVED (Erdős's conjecture holds). Topics: number theory, additive basis. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_ec48b4d42f615c0f | Erdős Problem #220 has been PROVED (Erdős's conjecture holds). Topics: number theory. Erdős prize: $500. Not yet formalized in Lean. OEIS: A322144. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_ec571c4dd3b41fc8 | Erdős Problem #568 remains OPEN. Topics: graph theory, ramsey theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_ec6bbbca1323ff9b | Erdős Problem #580 has status 'decidable'. Topics: graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_ec7f221a05d90167 | Erdős Problem #168 remains OPEN. Topics: additive combinatorics. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A004059, A057561, A094708, A386439. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_ecabb6f9f6b94457 | Erdős Problem #576 remains OPEN. Topics: graph theory, turan number. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_ecf3b8c85691a239 | Erdős Problem #1159 remains OPEN. Topics: combinatorics. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_ecf77211572d99cc | Erdős Problem #738 remains OPEN. Topics: graph theory, chromatic number. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_eda8dd0de2f55eb7 | Erdős Problem #253 has been DISPROVED (a counterexample is known). Statement: Let $a_1 < a_2 < \dotsc$ be an infinite sequence of positive integers such that $\frac{a_{i+1}}{a_i} \to 1$. If every arithmetic progression contains infinitely many integers which are the sum of distinct $a_i$ then every sufficiently large integer is the sum of distinct $a_i$. Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_edb314f45838fa69 | Erdős Problem #198 has status 'disproved (lean)'. Statement: The answer is no; Erdős and Graham report this was proved by Baumgartner, presumably referring to the paper [Ba75], which does not state this exactly, but the following simple construction is implicit in [Ba75]. Let $P_1,P_2,\ldots$ be an enumeration of all countably many infinite arithmetic progressions. We choose $a_1$ to be the minimal element of $P_1\cap \mathbb{N}$, and in general choose $a_n$ to be an element of $P_n\cap \mathbb{N}$ such that $a_n>2a_{n-1}$. By construction $A=\{a_1 < a_2 < \cdots\}$ contains at least one element from every infinite arithmetic progression, and is a lacunary set, so is certainly Sidon. AlphaProof has found the following explicit construction: $A = \{ (n+1)!+n : n\geq 0\}$. This is a Sidon set, and intersects every arithmetic progression, since for any $a,d\in \mathbb{N}$, $(a+d+1)!+(a+d)\in A$, and $d$ divides $(a+d+1)!+d$. This was formalized in Lean by Alexeev using Aristotle. Topics: additive combinatorics, sidon sets, arithmetic progressions. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_ede0b0cddd2bbaab | Erdős Problem #982 has status 'falsifiable'. Statement: If $n$ distinct points in $\mathbb{R}^2$ form a convex polygon then some vertex has at least $\lfloor\frac{n}{2}\rfloor$ different distances to other vertices. Topics: geometry, convex, distances. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A004526. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_ee044f4d4a4f247e | Erdős Problem #753 has status 'disproved (lean)'. Topics: graph theory, chromatic number. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_ee19502debcf9c87 | Erdős Problem #879 remains OPEN. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: A186736. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_ee31a48b01f979bc | Erdős Problem #31 has status 'proved (lean)'. Topics: number theory, additive basis. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_eea98437964cac5e | Erdős Problem #1173 remains OPEN. Topics: set theory, combinatorics. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_eecf9cbc59b63eda | Erdős Problem #1055 remains OPEN. Statement: A prime $p$ is in class $1$ if the only prime divisors of $p+1$ are $2$ or $3$. In general, a prime $p$ is in class $r$ if every prime factor of $p+1$ is in some class $\leq r-1$, with equality for at least one prime factor. Are there infinitely many primes in each class? Topics: number theory, primes. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A005113. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_ef04fc130d140a08 | Erdős Problem #784 is SOLVED. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_ef1812690869d36a | Erdős Problem #137 remains OPEN. Statement: Let $k\geq 3$. Can the product of any $k$ consecutive integers $N$ ever be powerful? That is, must there always exist a prime $p\mid N$ such that $p^2\nmid N$? Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_ef3680c82f6c6366 | Erdős Problem #943 remains OPEN. Statement: Let $A$ be the set of powerful numbers. Is is true that $1_A\ast 1_A(n)=n^{o(1)}$ for every $n$? Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_ef4420e794c43a96 | Erdős Problem #524 remains OPEN. Topics: analysis, probability, polynomials. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_ef4d3472e4e874c1 | Erdős Problem #674 has status 'proved (lean)'. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_ef64033868f51c92 | Erdős Problem #1066 remains OPEN. Topics: graph theory, planar graphs. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_ef7066987d658f0e | OBLIGATION (Erdos #488). BANKED: per-fixed-A exact decision certificates (7500+ antichains, zero counterexamples). OPEN: no uniform proof: the per-A certificates do not combine into a statement for all A. | unreviewed | 0.50 | — | — | asserted · 2d |
| vf_ef8655298ddcf944 | Erdős Problem #971 remains OPEN. Statement: Let `p(a, d)` be the least prime congruent to `a (mod d)`. Does there exist a constant `c > 0` such that for all large `d`, `p(a, d) > (1 + c) * φ(d) * log d` for `≫ φ(d)` many values of `a`? Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A226521. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_ef974a0b958ed0ef | Erdős Problem #452 remains OPEN. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_efeaae8784edc61f | Erdős Problem #852 remains OPEN. Topics: number theory, primes. Erdős prize: no. Not yet formalized in Lean. OEIS: A001223, A053597, A078515. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_f0526b9fdc0179a6 | Erdős Problem #85 remains OPEN. Statement: Is it true that, for all large $n$, $f(n + 1) \ge f(n)$? Topics: graph theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A006672, possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_f08849559bdd911a | Erdős Problem #676 remains OPEN. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: A390181, in progress. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_f0dc1c979545eb50 | Erdős Problem #806 has been PROVED (Erdős's conjecture holds). Topics: additive combinatorics. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_f0eff5b0327a808d | Erdős Problem #169 remains OPEN. Topics: additive combinatorics, arithmetic progressions. Erdős prize: no. Not yet formalized in Lean. OEIS: A005346. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_f101bd8f72471c22 | Erdős Problem #48 has been PROVED (Erdős's conjecture holds). Statement: Are there infinitely many integers $n, m$ such that $ϕ(n) = σ(m)$? Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_f13eeefb4521aaad | Erdős Problem #731 remains OPEN. Topics: number theory, binomial coefficients. Erdős prize: no. Not yet formalized in Lean. OEIS: A006197. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_f16fcdca9d3a5803 | Erdős Problem #412 remains OPEN. Statement: Let $σ_1(n)=σ(n)$, the sum of divisors function, and $σ_k(n) = σ(σ_{k-1}(n))$. Is it true that, for every $m, n ≥ 2$, there exist some $i, j$ such that $σ_i(m) = σ_j(n)$? Topics: number theory, iterated functions. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A007497, A051572. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_f19675ec55ccefb9 | Erdős Problem #257 remains OPEN. Statement: Let $A\subseteq\mathbb{N}$ be an infinite set. Is $$ \sum_{n\in A} \frac{1}{2^n - 1} $$ irrational? Topics: irrationality. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_f1e934349223eb09 | Erdős Problem #346 remains OPEN. Statement: Is it true that for every lacunary, strongly complete sequence `A` that is not complete whenever infinitely many terms are removed from it, `lim A (n + 1) / A n = (1 + √5) / 2`? Topics: number theory, complete sequences. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_f211388aef28d720 | Erdős Problem #1156 remains OPEN. Topics: graph theory, chromatic number. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_f21ecf9c79aeefa8 | Erdős Problem #439 has been PROVED (Erdős's conjecture holds). Topics: number theory, ramsey theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_f2b6734f4018b2ad | Erdős Problem #326 remains OPEN. Statement: Let $A \subset \mathbb{N}$ be an additive basis of order 2. Must there exist $B = \{b_1 < b_2 < \dots\} \subseteq A$ which is also a basis such that $\lim_{k\to\infty} \frac{b_k}{k^2}$ does not exist? Topics: number theory, additive basis. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_f2d800ee168df1e6 | Erdős Problem #148 remains OPEN. Topics: number theory, unit fractions. Erdős prize: no. Not yet formalized in Lean. OEIS: A076393, A006585. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_f2dd18709a77c538 | Erdős Problem #445 remains OPEN. Statement: Is it true that, for any $c>1/2$, if $p$ is a sufficiently large prime then, for any $n\geq 0$, there exist $a,b\in(n,n+p^c)$ such that $ab\equiv 1\pmod{p}$? This is discussed in this MathOverflow question [MathOverflow]. Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_f308e6cad2131c2d | Erdős Problem #212 remains OPEN. Statement: Is there a dense subset of ℝ^2 such that all pairwise distances are rational? Topics: geometry, distances. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_f33fdf491c4e825b | Erdős Problem #464 has been PROVED (Erdős's conjecture holds). Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_f370fa0545690e9e | Erdős Problem #170 remains OPEN. Topics: additive combinatorics. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A046693. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_f3751bf099d9bb56 | Erdős Problem #938 remains OPEN. Statement: Let $A=\{n_1 < n_2 < \cdots\}$ be the sequence of powerful numbers (if $p\mid n$ then $p^2\mid n$). Are there only finitely many three-term progressions of consecutive terms $n_k,n_{k+1},n_{k+2}$? Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A001694, possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_f3d53f6c9139a26e | Erdős Problem #1064 has been PROVED (Erdős's conjecture holds). Statement: Let $ϕ(n)$ be the Euler's totient function, then the $n$ satisfies $ϕ(n)>ϕ(n - ϕ(n))$ have asymptotic density 1. Reference: [LuPo02] Luca, Florian and Pomerance, Carl, On some problems of {M}\polhk akowski-{S}chinzel and {E}rd\H os concerning the arithmetical functions {$\phi$} and {$\sigma$}. Colloq. Math. Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A051488, A051487. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_f46e127c8e838c22 | Erdős Problem #280 has status 'disproved (lean)'. Topics: number theory, covering systems. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_f4a6af6fceba2f9a | Erdős Problem #110 has been DISPROVED (a counterexample is known). Topics: graph theory, chromatic number, cycles. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_f4af76055209929c | Erdős Problem #1003 remains OPEN. Statement: Are there infinitely many solutions to $\phi(n) = \phi(n+1)$, where $\phi$ is the Euler totient function? Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A001274. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_f4b7334de818a37d | Erdős Problem #1005 remains OPEN. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: A386893. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_f4c2721709671b7c | Erdős Problem #796 remains OPEN. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_f4caa6e2f91dd023 | Erdős Problem #1186 remains OPEN. Topics: additive combinatorics, arithmetic progressions. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_f4e425d5c0572fc0 | Erdős Problem #120 remains OPEN. Statement: Let $A \subseteq \mathbb{R}$ be an infinite set. Must there be a set $E \subseteq \mathbb{R}$ of positive measure which does not contain any set of the shape $a * A + b$ for some $a,b \in \mathbb{R}$ and $a \neq 0$? Topics: combinatorics. Erdős prize: $100. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_f4f45c3816bc5e38 | Erdős Problem #526 is SOLVED. Topics: probability, geometry. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_f5247fb48814efa1 | Erdős Problem #301 remains OPEN. Topics: number theory, unit fractions. Erdős prize: no. Not yet formalized in Lean. OEIS: A390394. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_f547ee8c78f0d4b8 | Erdős Problem #300 is SOLVED. Topics: number theory, unit fractions. Erdős prize: no. Not yet formalized in Lean. OEIS: A390393. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_f64b9cd7d1cf6002 | Erdős Problem #851 has been PROVED (Erdős's conjecture holds). Statement: Let $\epsilon > 0$. Is there some $r \ll_\epsilon 1$ such that the density of integers of the form $2^k+n$, where $k \geq 0$ and $n$ has at most $r$ prime divisors, is at least $1-\epsilon$? This was proved affirmatively by Price and GPT-5.2 Pro [Pr26]. Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_f65e272482ffd103 | Erdős Problem #883 remains OPEN. Topics: number theory, graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_f684f1d5bed75e1a | Erdős Problem #945 remains OPEN. Statement: Is it true that $F(x) \leq (\log x)^{O(1)}$? Topics: number theory, divisors. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: possible, A048892. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_f6e889c690621887 | Erdős Problem #24 has status 'proved (lean)'. Topics: graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_f730a1f4ef78b348 | Erdős Problem #492 has been DISPROVED (a counterexample is known). Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_f73ab0e09ed4c7e7 | Erdős Problem #1189 remains OPEN. Topics: number theory, covering systems. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_f7af199e72ace90b | Erdős Problem #790 remains OPEN. Topics: additive combinatorics. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_f7ef90745a29322b | Erdős Problem #1107 remains OPEN. Statement: Let $r \ge 2$. Is every large integer the sum of at most $r + 1$ many $r$-powerful numbers? Topics: number theory, powerful. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A056828, A392342, A392343, possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_f83b032cfff7b525 | Erdős Problem #271 remains OPEN. Topics: additive combinatorics, arithmetic progressions. Erdős prize: no. Not yet formalized in Lean. OEIS: A005487. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_f8db7c479bde8c67 | Erdős Problem #998 has been PROVED (Erdős's conjecture holds). Topics: analysis, diophantine approximation. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_f8fd3ed0562f3ca8 | Erdős Problem #306 remains OPEN. Statement: Let $\frac a b\in \mathbb{Q}_{>0}$ with $b$ squarefree. Are there integers $1 < n_1 < \dots < n_k$, each the product of two distinct primes, such that $\frac{a}{b}=\frac{1}{n_1}+\cdots+\frac{1}{n_k}$? Topics: number theory, unit fractions. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_f90f618330d42b84 | Erdős Problem #57 has been PROVED (Erdős's conjecture holds). Topics: graph theory, chromatic number, cycles. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_f91e5876c643b8a0 | Erdős Problem #196 remains OPEN. Statement: Must every permutation of $\mathbb{N}$, contain a monotone 4-term arithmetic progression? Topics: arithmetic progressions. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_f9ea4680dd32abb9 | Erdős Problem #1108 remains OPEN. Topics: number theory, factorials. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A051761, A115645, A025494. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_fa406ad83a5063e3 | Erdős Problem #284 has been PROVED (Erdős's conjecture holds). Topics: number theory, unit fractions. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_fa5de8ceb47e2f35 | Erdős Problem #165 remains OPEN. Topics: graph theory, ramsey theory. Erdős prize: $250. Not yet formalized in Lean. OEIS: A000791. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_fa5fac087a318e53 | Erdős Problem #1194 remains OPEN. Topics: additive combinatorics, additive basis, sidon sets. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_fa8becfc1b6cd5f5 | Erdős Problem #926 has been PROVED (Erdős's conjecture holds). Topics: graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_fad83efc61e40a53 | Erdős Problem #672 has status 'verifiable'. Statement: Can the product of an arithmetic progression of positive integers $n, n + d, ..., n + (k - 1)d$ of length ≥ 4, with $(n, d) = 1$, be a perfect power? Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_fb2741c42fe49d67 | Erdős Problem #669 remains OPEN. Topics: geometry. Erdős prize: no. Not yet formalized in Lean. OEIS: A003035, A006065, A008997, possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_fb6179db3c75c710 | Erdős Problem #1091 is SOLVED. Topics: geometry, chromatic number. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_fb93d52e3f8396a7 | Erdős Problem #827 remains OPEN. Topics: geometry. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_fbc960d372f9c7c7 | Erdős Problem #264 remains OPEN. Topics: irrationality. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_fc38d9b1dda9ae8c | Erdős Problem #508 remains OPEN. Topics: geometry, ramsey theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_fc9225344ea0d129 | Erdős Problem #954 remains OPEN. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: A390642. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_fcb6d74734d8b01f | Erdős Problem #785 has status 'proved (lean)'. Topics: additive combinatorics. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_fcb8f22cb7a61ef9 | Erdős Problem #786 remains OPEN. Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A143301, possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_fccad3dc897074b9 | Erdős Problem #501 remains OPEN. Statement: For every $x \in \mathbb{R}$ let $A_x \subset \mathbb{R}$ be a bounded set with outer measure $< 1$. Must there exist an infinite independent set, that is, some infinite $X \subseteq \mathbb{R}$ such that $x \notin A_y$ for all $x \neq y \in X$? If the sets $A_x$ are closed and have measure $< 1$, then must there exist an independent set of size $3$? Known results: Erdős–Hajnal [ErHa60] proved the existence of arbitrarily large finite independent sets. Hechler [He72] showed the answer is **no** assuming the continuum hypothesis. Topics: combinatorics, set theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_fcfdd50f796c217d | Erdős Problem #435 has status 'proved (lean)'. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: A389479. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_fd45fd49d7d57f1c | Erdős Problem #1120 remains OPEN. Topics: analysis. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_fd79671bb09c9c65 | Erdős Problem #680 remains OPEN. Topics: number theory, primes. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_fd8ab3e64a757ee9 | Erdős Problem #860 remains OPEN. Topics: number theory, primes. Erdős prize: no. Not yet formalized in Lean. OEIS: A048670, A058989. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_fde30edf3b650afc | Erdős Problem #374 remains OPEN. Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: A388851, A387184, A389117, A389148. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_fdefab44fc6b2e27 | Erdős Problem #1176 has status 'not disprovable'. Statement: Let $G$ be a graph with chromatic number $\aleph_1$. Is it true that there is a colouring of the edges with $\aleph_1$ many colours such that, in any countable colouring of the vertices, there exists a vertex colour containing all edge colours? A problem of Erdős, Galvin, and Hajnal. The consistency of this was proved by Hajnal and Komjáth. Topics: set theory, chromatic number. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_fe3dc3c53ca73aa7 | Erdős Problem #578 has been PROVED (Erdős's conjecture holds). Topics: graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_fe7082ef9ece1fe0 | Erdős Problem #807 has been DISPROVED (a counterexample is known). Topics: graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_fe7667165a5ff891 | Erdős Problem #132 remains OPEN. Topics: distances. Erdős prize: $100. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_feaad1f6a7b5f3c2 | Erdős Problem #1129 has been PROVED (Erdős's conjecture holds). Topics: analysis, polynomials. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_febc1207a032af15 | Erdős Problem #759 is SOLVED. Topics: graph theory, chromatic number. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_ff129c675df87cfb | Erdős Problem #837 remains OPEN. Topics: graph theory, hypergraphs. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_ff17e9912e2bd1f3 | Erdős Problem #373 remains OPEN. Statement: Show that the equation `n!=a_1!a_2!···a_k!`, with `n−1 > a_1 ≥ a_2 ≥ ··· ≥ a_k`, has only finitely many solutions. Topics: number theory, factorials. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A003135. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_ff32c86766427fc4 | Erdős Problem #722 has been PROVED (Erdős's conjecture holds). Topics: combinatorics. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_ff49e066608f6dc4 | Erdős Problem #757 remains OPEN. Statement: What is the supremum of the set of admissible numbers? Topics: geometry, distances, sidon sets. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_ff651a691e750f99 | Erdős Problem #421 remains OPEN. Statement: Is there a sequence $1 \le d_1 < d_2 < \dots$ with density 1 such that all products $\prod_{u \le i \le v} d_i$ are distinct? Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A389544, A390848. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_ff69437d47ca4fb3 | Erdős Problem #475 has status 'decidable'. Topics: number theory, additive combinatorics. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_ff825c76a7d83fbd | Erdős Problem #87 remains OPEN. Topics: graph theory, ramsey theory. Erdős prize: no. Not yet formalized in Lean. OEIS: A059442, possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_ffbcf567afda74fe | Erdős Problem #549 has been DISPROVED (a counterexample is known). Topics: graph theory, ramsey theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_ffd1943974b46af5 | Erdős Problem #98 remains OPEN. Statement: Let $h(n)$ be such that any $n$ points in $\mathbb{R}^2$, with no three on a line and no four on a circle, determine at least $h(n)$ distinct distances. Does $h(n)/n\to \infty$? Topics: geometry, distances. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: possible. | unreviewed | 0.99 | — | — | asserted · 13d |
| vf_ffe8ddb4af2a1f69 | Erdős Problem #547 has status 'decidable'. Topics: graph theory, ramsey theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. | unreviewed | 0.99 | — | — | asserted · 13d |