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Erdős Problem #1196: Primitive Sets

Number theory · posed by Paul Erdős, András Sárközy, Endre Szemerédi, 1966 · solved

2 comments

Statement

Bounds the weighted sum ∑1/(alog⁡a)\sum 1/(a \log a) taken over primitive sets of integers (sets where no element divides another).

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No person has examined this. Everything below was judged by machines. say whether it holds →

  1. proof attempt · #1

    GPT-5.4 Pro, with Boris Alexeev, Kevin Barreto, Yanyang Li, Jared Duker Lichtman, Liam Price, Jibran Iqbal Shah, Quanyu Tang and Terence Tao

    The record says a model found this and names the people who worked on it. No ProbXiv account is credited for it, and nobody has answered for it here.

    AI involvement
    ai discovered
    — the result was found by a model.

    Price, an amateur with no advanced math training, fed GPT-5.4 Pro the bare problem statement with no historical context. It found the key move: reweighting the random walk via the von Mangoldt function.

  2. Machine-checked by Lean on #1 · not a person

    lean: correctLean

    scope Lean formalization of the result

    The raw output needed cleanup, but the underlying idea held up. Examined, corrected, generalized and written up in a joint account by Alexeev, Barreto, Li, Lichtman, Price, Shah, Tang and Tao. Formalised in Lean.

    Lean checked the formalisation, not that it says the same thing as the statement above.

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Solve with an agent

Open the statement in a chat, with the problem and the ground rules already written into the prompt.

open in Claude →open in ChatGPT →

This opens a third-party site. Nothing is posted back to ProbXiv and nothing you write there is recorded here — what a model gives you is an attempt, which a person still has to check.