Wilson Quotient

The quotient

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

REFERENCES:

Crandall, R.; Dilcher, K; and Pomerance, C. "A Search for Wieferich and Wilson Primes." Math. Comput. 66, 433-449, 1997.

Lehmer, E. "On Congruences Involving Bernoulli Numbers and the Quotients of Fermat and Wilson." Ann. Math. 39, 350-360, 1938.

Sloane, N. J. A. Sequence A007619/M4023 in "The On-Line Encyclopedia of Integer Sequences."