Pillai prime
If for a given prime $p$ we can find an integer $n>0$ such that $n!\equiv -1modp$ but $p\not\equiv 1modn$ then $p$ is a called a Pillai prime. These are listed in A063980 of Sloane’s OEIS. Sarinya Intaraprasert proved that there are infinitely many Pillai primes. The first few are 23, 29, 59, 61, 67, 71, 79, 83, 109, 137, 139, 149, 193, …
References
- 1 R. K. Guy, Unsolved Problems in Number Theory^{} New York: Springer-Verlag 2004: A2
Title | Pillai prime |
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Canonical name | PillaiPrime |
Date of creation | 2013-03-22 16:33:14 |
Last modified on | 2013-03-22 16:33:14 |
Owner | PrimeFan (13766) |
Last modified by | PrimeFan (13766) |
Numerical id | 5 |
Author | PrimeFan (13766) |
Entry type | Definition |
Classification | msc 11A41 |