# weak prime

If for the given $n$th prime ${p}_{n}$ the inequality^{}

$$ |

is true, then ${p}_{n}$ is said to be a weak prime. That is, the arithmetic mean^{} of the given prime, the prime immediately below and the one immediately above, is more than the middle prime. The first few are 3, 7, 13, 19, 23, 31, 43, 47, 61, 73, 83, 89, listed in A051635 of Sloane’s OEIS.

Title | weak prime |
---|---|

Canonical name | WeakPrime |

Date of creation | 2013-03-22 16:36:56 |

Last modified on | 2013-03-22 16:36:56 |

Owner | PrimeFan (13766) |

Last modified by | PrimeFan (13766) |

Numerical id | 4 |

Author | PrimeFan (13766) |

Entry type | Definition |

Classification | msc 11A41 |

Related topic | BalancedPrime |

Related topic | StrongPrime |