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Erdős Problem #997

Number theory · posed by Paul Erdős, 1964 · solved

1 attempt · 1 machine check

Statement

VibeMathed records no statement for this problem. See erdosproblems.com for the original.

Context

A numbered Erdos problem that an unusually dense reference trail on erdosproblems.com (6 sources), setting it above the typical entry in the catalog.

People

Attempts

1 attempt

No person has examined this. There is 1 attempt here and 1 machine check recorded against it. A machine check is a judgement recorded by a tool: no account is credited for it, nobody has put their name to it, and it is not verification by a person. Saying whether the mathematics holds is the most useful thing anybody can do on this page.

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  • #1

    Attempt 1

    proof attemptOpenAI internal model with Boris Alexeev, Moe Putterman, Mehtaab Sawhney, Mark Sellke, Gregory Valiant ·
    AI involvement
    ai discovered
    the result was found by a model.
    models
    OpenAI internal model
    people
    Boris Alexeev, Moe Putterman, Mehtaab Sawhney, Mark Sellke, Gregory Valiant

    From "Short proofs in combinatorics and number theory": "In each case, the proof is due entirely to an internal model at OpenAI. The role of the human authors was simply to digest the proofs and modify the write-ups for clarity and elegance." This entry's solve is that paper's Theorem 4.1, proving that for every real alpha the sequence of fractional parts of alpha times the primes is not well-distributed.

    Reviews

    1 machine check

    No person has reviewed this attempt. 1 machine check below — a machine check is not human verification.

    • Machine check · not human verification

      machine: correct

      Recorded from Lean ·

      scope Lean formalization of the result

      Listed as solved on erdosproblems.com and the proof is verified in Lean. Solve credited via Terence Tao's AI-contributions wiki.

      No ProbXiv account is credited for this check. Nobody has put their name to it, so it carries no personal accountability and does not count as verification by a person.

    Discussion of this attempt

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