# factorial prime

A factorial prime^{} is a number that is one less or one more than a factorial^{} and is also a prime number^{}. The first few factorial primes are: 2, 3, 5, 7, 23, 719, 5039, 39916801, 479001599, 87178291199 (sequence A088054 in the OEIS). It is conjectured that only for $n=3$ are both $n!-1$ and $n!+1$ both primes.

Factorial primes have a rĂ´le in an argument that 1 is not a prime number. If $n$ is a positive integer and $p$ is a prime number, $n!+p$ is never a prime for $$, because obviously it will be a multiple^{} of $p$, just as $n!$ is. But $n!+1$, even though it certainly is a multiple of 1, can be a prime, specifically, a factorial prime. (The same is also true if we subtract instead of add).

Title | factorial prime |
---|---|

Canonical name | FactorialPrime |

Date of creation | 2013-03-22 16:19:19 |

Last modified on | 2013-03-22 16:19:19 |

Owner | PrimeFan (13766) |

Last modified by | PrimeFan (13766) |

Numerical id | 6 |

Author | PrimeFan (13766) |

Entry type | Definition |

Classification | msc 11A41 |

Classification | msc 05A10 |

Classification | msc 11B65 |