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Binary Digits of the Erdős-Borwein Constant

Number theory · posed by Richard Crandall, 2012 · solved

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Statement

Does the block 1111 occur infinitely often in the base-22 expansion of the Erdős-Borwein constant E=∑n≥112n−1E = \sum_{n \ge 1} \frac{1}{2^n - 1}? Posed by Crandall in 2012.

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

  1. proof attempt · #1

    John M. Campbell, using GPT-5.5 Pro

    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 proof - a congruence construction in the spirit of Erdős combined with the Alford-Granville-Pomerance estimate for primes in arithmetic progressions - was developed through extensive interactions with GPT-5.5 Pro.

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