Wilson prime
In
mathematics, a
Wilson prime is a certain kind of
prime number. A prime
p is called a Wilson prime if
p² divides (
p − 1)! + 1, where ! denotes the
factorial function; compare this with
Wilson's theorem, which states that every prime
p divides (
p − 1)! + 1.
The only known Wilson primes are 5, 13, and 563 (Sloane's A007540); if any others exist, they must be > 5 · 108. It has been conjectured that infinitely many Wilson primes exist, and that the number of Wilson primes in an interval [x, y] is about log(log(y) / log(x)).
Also see
External links