Wilson Quotient

The quotient


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).

See also

Prime Formulas, Wilson Prime

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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."

Referenced on Wolfram|Alpha

Wilson Quotient

Cite this as:

Weisstein, Eric W. "Wilson Quotient." From MathWorld--A Wolfram Web Resource.

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