The quotient W(p) congruent ((p - 1)! + 1)/p which must be congruent to 0 (mod p) for p to be a Wilson prime. The quotient is an integer only when p = 1 (in which case W(1) = 2) or p is a prime, and the values of W(p) corresponding to p = 2, 3, 5, 7, 11, ... are 1, 1, 5, 103, 329891, 36846277, 1230752346353, ... (OEIS A007619).

prime formulas | Wilson prime