Wilson prime

If for a given prime $p$ it is true that $(p-1)!\equiv -1mod{p}^2$, then $p$ is called a Wilson prime. Like all other primes, Wilson primes satisfy the primality condition of Wilson’s theorem, but they also divide the Wilson quotient. Only three are known as of 2007, namely: 5, 13, 563 (A007540 in Sloane’s OEIS, which normally requires at least four terms before accepting sequences into the table). It is not known if there are infinitely many Wilson primes exist; the fourth Wilson prime would have to be greater than ${10}^9$.

Title	Wilson prime
Canonical name	WilsonPrime
Date of creation	2013-03-22 16:40:39
Last modified on	2013-03-22 16:40:39
Owner	PrimeFan (13766)
Last modified by	PrimeFan (13766)
Numerical id	5
Author	PrimeFan (13766)
Entry type	Definition
Classification	msc 11A41