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 ; 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 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
• MathWorld: Wilson prime
• Status of the search for Wilson primes

Prime numbers | Factorial and binomial topics

Wilson-Primzahl | Nombre de Wilson | מספר ראשוני וילסון | 威爾遜質數