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Composites Among [ξ 7^n] and Right-Truncatable Primes in Base 7

Number theory · posed by Forman and Shapiro (1967), Dubickas and Novikas (2005), 2005 · solved

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Statement

For every real ξ>0\xi>0 the sequence of integer parts [ξ7n][\xi 7^{n}], n=0,1,2,…n=0,1,2,\dots, contains infinitely many composite numbers. Second, there is no infinite right truncatable prime in base~77.

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

  1. computation · #1

    Fable 5, Opus 4.8

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

    After showing that a finite computation can provably resolve the problem, it wrote programs to do the computation, resulting in a checkable certificate. It then was directed to formalize all proofs and the certificate check in Lean. Finally it was directed to write a draft of the paper from the Lean.

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