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Wilson prime |  | Wilson prime: Encyclopedia - Wilson prime |  | | 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 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, ...
|  | | Wilson prime, Wieferich prime, Wall-Sun-Sun prime, Wolstenholme prime |  | |
|  |  | Wilson prime: Encyclopedia - Wilson prime
Wilson prime
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 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
Other related archives13, 5, OEIS, Wall-Sun-Sun prime, Wieferich prime, Wilson's theorem, Wolstenholme prime, conjectured, factorial function, mathematics, prime number
 Adapted from the Wikipedia article "Wilson prime", under the G.N U Free Docmentation License. Please also see http://en.wikipedia.org/wiki |
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