# Wilson prime

If for a given prime $p$ it is true that $(p-1)!\equiv-1\mod p^{2}$, then $p$ is called a . 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 WilsonPrime 2013-03-22 16:40:39 2013-03-22 16:40:39 PrimeFan (13766) PrimeFan (13766) 5 PrimeFan (13766) Definition msc 11A41