On Mar 8, 12:13 am, m...@vex.net (Mark Brader) wrote: > > How many positive integers n are there such that n! + 1 is > > composite? > > Infinitely many, or to be more specific, aleph-null. > > Wilson's theorem states that if p is prime, then (p-1)! + 1 is > divisible by p. If x > 3, then (x-1)! + 1 > x. Therefore the > desired property holds for all numbers n > 4 where n-1 is prime, > and there are aleph-null of those.