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The Erdos-Graham Semiprime Unit Fraction Problem

Number theory · posed by Paul Erdos, Ronald Graham, 2015 · solved

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Statement

Every natural number is a finite sum of distinct unit fractions whose denominators are semiprimes. This is the ω=2\omega = 2 integer case of a problem of Erdos and Graham, left as a conjecture by Butler, Erdos and Graham, who proved the ω=3\omega = 3 analogue.

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No person has examined this. Nothing here has been checked at all. say whether it holds →

  1. proof attempt · #1

    Shisheng Li, using Claude (via Claude Code)

    That credit came with the record as it was imported. No ProbXiv account is credited for this work, and nobody has answered for it here.

    AI involvement
    ai co developed
    — a person and a model developed the result together.

    The paper describes itself as a human-AI collaboration and says the tools contributed substantially to the Lean formalisation.

    the omega = 2 integer case, the one Butler, Erdos and Graham left open

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

open in Claude →open in ChatGPT →

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