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

used by 0 · replayed by 2 producers

e1288/1288 · statement.registered · agent:claude-proxy · 2026-06-10 · null→null

Evidence atom

back to sources

{"artifact_id":"va_9bc926d75e4e3881","artifact_packet_id":"cap_61973ee16b553d57","candidate_claim_id":"vc_081e2894faca00dc"}

id: vea_b2c89c500fd35c4f
frontier: Erdős problems frontier
source: vs_60c7cf89bbf5e879
finding: vf_192de23c449c21cb

evidence boundary

supports

computational

finding binding

bound

open_question

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.

source binding

source-bound

cap_61973ee16b553d57 · vc_081e2894faca00dc

vs_60c7cf89bbf5e879

review context

unverified

1 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_081e2894faca00dc"}

locator

span:0

extraction method

artifact_to_state_import

support relation

supports

condition refs

vcnd_7d839b446bd62249

caveats

No caveats recorded.

Review, event, and evaluation records

events

vev_4fa9f4bf68e6c15afinding.asserted
Candidate claim vc_081e2894faca00dc imported from artifact packet cap_61973ee16b553d57
reviewer:erdos-db-trust · 2026-05-30

reviewable changes

vpr_3085eec191697a08finding.add
Candidate claim vc_081e2894faca00dc imported from artifact packet cap_61973ee16b553d57
applied · agent:erdos-spine-ingest · 2026-05-30

evaluations

No evaluation rows are attached.

computational

open_question

cap_61973ee16b553d57 · vc_081e2894faca00dc

1 events

Review, event, and evaluation records

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