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arXiv · 2410.03677

No new Goormaghtigh primes up to $10^{700}$

Jon Grantham
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Abstract

The Goormaghtigh conjecture states that the only two numbers which have two non-trivial representations as repunits are $31$ and $8191$. We call such a prime number a {\it Goormaghtigh prime}. We show that there are no other Goormaghtigh primes less than $10^{700}$.

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Jon Grantham. 2024-09-19. No new Goormaghtigh primes up to $10^{700}$. https://arxiv.org/abs/2410.03677

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