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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

1 attempt

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.

Context

A concrete question in the Forman-Shapiro tradition, posed for base 7 by Dubickas and Novikas in 2005 and open twenty-one years. Specialist but genuinely standing - level with the numbered-Erdos band at 10.

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Attempts

1 attempt

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  • #1

    Attempt 1

    computationFable 5, Opus 4.8 ·
    AI involvement
    ai discovered
    the result was found by a model.
    models
    Fable 5, Opus 4.8

    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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