Wilson prime

Wilson prime

A Wilson prime is a prime number "p" such that "p"² 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 OEIS|id=A007540; if any others exist, they must be greater than 5e|8. 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

* [http://primes.utm.edu/glossary/page.php?sort=WilsonPrime The Prime Glossary: Wilson prime]
* [http://www.loria.fr/~zimmerma/records/Wieferich.status Status of the search for Wilson primes]

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