The Wilson quotient "W"("p") is defined as:
formula_1
If "p" is a prime number, the quotient is an integer by Wilson's theorem; moreover, if "p" is composite, the quotient is not an integer. If "p" divides "W"("p"), it is called a Wilson prime. The integer values of "W"("p") are (sequence in the OEIS):
 "W"(2) = 1
 "W"(3) = 1
 "W"(5) = 5
 "W"(7) = 103
 "W"(11) = 329891
 "W"(13) = 36846277
 "W"(17) = 1230752346353
 "W"(19) = 336967037143579
It is known that
formula_2
formula_3
where formula_4 is the "k"-th Bernoulli number. Note that the first relation comes from the second one by subtraction, after substituting formula_5 and formula_6.