# balanced prime

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

$${p}_{n}=\frac{1}{3}\sum _{i=n-1}^{n+1}{p}_{i}$$ |

is true, then ${p}_{n}$ is said to be a balanced prime. That is, the arithmetic mean^{} of the given prime, the prime immediately below and the one immediately above, is equal to the middle prime. The first few are 5, 53, 157, 173, 211, 257, 263, 373, listed in A006562 of Sloane’s OEIS. As of 2006, the largest known balanced prime is $197418203\times {2}^{25000}-1$, discovered by David Broadhurst and FranÃÂ§ois Morain using FastECPP and PrimeForm.

Title | balanced prime |
---|---|

Canonical name | BalancedPrime |

Date of creation | 2013-03-22 16:36:50 |

Last modified on | 2013-03-22 16:36:50 |

Owner | PrimeFan (13766) |

Last modified by | PrimeFan (13766) |

Numerical id | 4 |

Author | PrimeFan (13766) |

Entry type | Definition |

Classification | msc 11A41 |

Related topic | StrongPrime |

Related topic | WeakPrime |