# Wilson prime

If for a given prime $p$ it is true that $(p-1)!\equiv -1mod{p}^{2}$, then $p$ is called a Wilson prime^{}. Like all other primes, Wilson primes satisfy the primality condition of Wilson’s theorem, but they also divide the Wilson quotient^{}. Only three are known as of 2007, namely: 5, 13, 563 (A007540 in Sloane’s OEIS, which normally requires at least four terms before accepting sequences into the table). It is not known if there are infinitely many Wilson primes exist; the fourth Wilson prime would have to be greater than ${10}^{9}$.

Title | Wilson prime |
---|---|

Canonical name | WilsonPrime |

Date of creation | 2013-03-22 16:40:39 |

Last modified on | 2013-03-22 16:40:39 |

Owner | PrimeFan (13766) |

Last modified by | PrimeFan (13766) |

Numerical id | 5 |

Author | PrimeFan (13766) |

Entry type | Definition |

Classification | msc 11A41 |