This criterion is based on Wilson’s Theorem.
Recall that Wilson’s Theorem states that a number (x) is prime if and only if (x-1)!+1)/x is an integer.
The generalization for twin primes goes like this If x is the lesser member of a twin prime pair then
(x-1)!+1)/x and (x-1)!+1)/(x+2) are both integers therefore the denominators are a twin prime pair.
Thank you,
Nungheaf
