Wilson prime

A Wilson prime is a prime number p such that 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 (sequence A007540 in OEIS); if any others exist, they must be greater than 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)).

See also

• Wieferich prime
• Wall-Sun-Sun prime
• Wolstenholme prime

External links

• The Prime Glossary: Wilson prime
• Eric W. Weisstein, Wilson prime at MathWorld.
• Status of the search for Wilson primes