It is not known if there are infinitely many Wilson primes. This question seems to be of such a character that if I should come to life any time after my death and some mathematician were to tell me that it had definitely been settled, I think I would immediately drop dead again.
[Wilson primes satisfy (p-1)! = -1 mod p2. 5, 13, and 563 are the only Wilson primes less than 5 x 108 ]
Quoted in D MacHale, Comic Sections (Dublin 1993)