Wilson quotient
The Wilson quotient W is defined as:
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, it is called a Wilson prime. The integer values of W are :
It is known that
where is the k-th Bernoulli number. Note that the first relation comes from the second one by subtraction, after substituting and.
