Wilson prime

Wilson primes ( after Sir John Wilson) are primes for which it holds a stronger form of the set of Wilson.

The set of Wilson says that is true for any prime number:

For notation see Faculty ( Mathematics ) and congruence ( number theory ).

A prime number is called Wilson prime if even

Applies. An equivalent formulation is: A prime number is called Wilson prime if

Applies. The left side, which is, by the theorem of Wilson is an integer, is referred to in this context as Wilson quotient ( sequence A007619 in OEIS ).

So far, only the Wilson primes 5, 13, and 563 ( Goldberg 1953) known ( sequence A007540 in OEIS ). If another Wilson primes exist, so it is greater than 5 × 108 It is believed that infinitely many exist Wilson primes, approximately between and.