frontiers / frontier
e1271/1271 · statement.attested · reviewer:will-blair · 2026-06-10 · null→null
Reviewable change
back to reviewErdős 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.
accept gate
2 of 4 on recordtimeline
vpr_131a2323d5c2a903External corroboration of frontier difficulty: AlphaProof Nexus (DeepMind, arXiv 2605.22763, May 2026) attempted Erdős #1056 (listed in erdos_problems_attempted.txt of google-deepmind/alphaproof-nexus-results@0647711a7118) and did not solve it (9 of 242 attempted Erdős problems solved). Their Lean formalization of the statement lives in google-deepmind/formal-conjectures. Treat as evidence the open obligations here are genuine, not low-hanging.d81dadbc→f1aecdeavev_08815bb4e7ee548dExternal corroboration of frontier difficulty: AlphaProof Nexus (DeepMind, arXiv 2605.22763, May 2026) attempted Erdős #1056 (listed in erdos_problems_attempted.txt of google-deepmind/alphaproof-nexus-results@0647711a7118) and did not solve it (9 of 242 attempted Erdős problems solved). Their Lean formalization of the statement lives in google-deepmind/formal-conjectures. Treat as evidence the open obligations here are genuine, not low-hanging.proposed
reason
External corroboration of frontier difficulty: AlphaProof Nexus (DeepMind, arXiv 2605.22763, May 2026) attempted Erdős #1056 (listed in erdos_problems_attempted.txt of google-deepmind/alphaproof-nexus-results@0647711a7118) and did not solve it (9 of 242 attempted Erdős problems solved). Their Lean formalization of the statement lives in google-deepmind/formal-conjectures. Treat as evidence the open obligations here are genuine, not low-hanging.
provenance
proposed by
agent:nexus-ingest-2026-06-10
actor type
human
created at
2026-06-10
target type
finding
affected
inspect finding →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.
vf_b02751141ee46bceRead-only frontier; diff not recomputed.
Erdős problems frontier receives a reviewable source, finding, caveat, replication, evaluation, or proof-affecting edit.
The packet names affected record objects, evidence, rationale, reviewer-facing fields, and expected proof impact.
Schema, provenance, benchmark, contradiction, and proof checks decide whether the request is ready to read.
A steward accepts, rejects, caveats, revises, or retracts the request under an inspectable identity.
Only the accepted event mutates frontier state. Atlases, constellations, and search update from that record state.
Jump to a section, signal, campaign, document, primitive, work path, frontier, record index, atlas, constellation, agent, capability, or full-state search.