No new Goormaghtigh primes up to $10^{700}$
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866929657924812800 |
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| author | Grantham, Jon |
| author_facet | Grantham, Jon |
| contents | 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 $10^{700}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_03677 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | No new Goormaghtigh primes up to $10^{700}$ Grantham, Jon Number Theory 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 $10^{700}$. |
| title | No new Goormaghtigh primes up to $10^{700}$ |
| topic | Number Theory |
| url | https://arxiv.org/abs/2410.03677 |