evidence boundary
supportsfrontiers / 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
Evidence atom
back to sources{"artifact_id":"va_9bc926d75e4e3881","artifact_packet_id":"cap_61973ee16b553d57","candidate_claim_id":"vc_e18a1401889f4ca1"}
- id
- vea_5662cf005c942bdb
- frontier
- Erdős problems frontier
- source
- vs_f44f5e2a875b0c9d
- finding
- vf_b3764125348b0dbb
finding binding
boundtheoretical
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.
source binding
source-boundcap_61973ee16b553d57 · vc_e18a1401889f4ca1
vs_f44f5e2a875b0c9d
review context
unverified1 events
1 reviewable changes and 0 evaluation records target this atom or its bound objects.
statement
{"artifact_id":"va_9bc926d75e4e3881","artifact_packet_id":"cap_61973ee16b553d57","candidate_claim_id":"vc_e18a1401889f4ca1"}
locator
span:0
extraction method
artifact_to_state_import
support relation
supports
condition refs
vcnd_0ca69b67e430b29a
caveats
No caveats recorded.
Review, event, and evaluation records
2events
vev_e3f10412a76e0c22finding.assertedCandidate claim vc_e18a1401889f4ca1 imported from artifact packet cap_61973ee16b553d57
reviewer:erdos-db-trust · 2026-05-30
reviewable changes
vpr_6f222f55a1d7313efinding.addCandidate claim vc_e18a1401889f4ca1 imported from artifact packet cap_61973ee16b553d57
applied · agent:erdos-spine-ingest · 2026-05-30
evaluations
No evaluation rows are attached.