For a prime, this quotient is congruent to 0 (mod ) iff is 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).
Crandall, R.; Dilcher, K.; and Pomerance, C. "A Search for Wieferich and Wilson Primes." Math. Comput.66, 433-449, 1997.
https://doi.org/10.1090/S0025-5718-97-00791-6.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."
is defined by
, this quotient is congruent to 0 (mod 
) iff 
is 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).
