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Binary Digits of the Erdős-Borwein Constant

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erdos-borwein-binary-blocksNumber theoryposed by Richard Crandall, 2012recorded: solved

1 attempt · no person has looked

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.

Context

A concrete question on a named constant, posed by Crandall.

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1 attempt

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  • #1

    Attempt 1

    proof attemptGPT-5.5 Pro with John M. Campbell ·
    AI involvement
    ai co developed
    — a person and a model developed the result together.
    models
    GPT-5.5 Pro
    people
    John M. Campbell

    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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