No new Goormaghtigh primes up to $10^{700}$
Number Theory
2025-01-07 v2
Abstract
The Goormaghtigh conjecture states that the only two numbers which have two non-trivial representations as repunits are and . We call such a prime number a {\it Goormaghtigh prime}. We show that there are no other Goormaghtigh primes less than .
Cite
@article{arxiv.2410.03677,
title = {No new Goormaghtigh primes up to $10^{700}$},
author = {Jon Grantham},
journal= {arXiv preprint arXiv:2410.03677},
year = {2025}
}
Comments
v2; published version + 1 typo corrected