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, …

Title	Pillai prime
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