Wilson prime

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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 (sequence 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]
• [MathWorld: Wilson prime]
• [Status of the search for Wilson primes]

 

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