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Wilson prime
A Wilson prime, named after English mathematician John Wilson, 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 ; if any others exist, they must be greater than 2.〔(A Search for Wilson primes ) Retrieved on November 2, 2012.〕 It has been conjectured that infinitely many Wilson primes exist, and that the number of Wilson primes in an interval () is about log(log(''y'')/log(''x'')).〔(The Prime Glossary: Wilson prime )〕
Several computer searches have been done in the hope of finding new Wilson primes.〔''A search for Wieferich and Wilson primes'', p 443〕
The Ibercivis distributed computing project includes a search for Wilson primes.〔(Ibercivis site )〕 Another search is coordinated at the mersenneforum.〔(Distributed search for Wilson primes ) (at mersenneforum.org)〕
==Generalizations==
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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