# Lucas-Lehmer primality test

Theorem: Let $p>2$ be a prime, and let ${M}_{p}$ be a Mersenne number, then ${M}_{p}$ is prime iff ${M}_{p}$ divides ${s}_{p-1}$ where the numbers ${({s}_{n})}_{n\ge 1}$ are given by the following recurrence relation^{}: ${s}_{1}=4$, and

$${s}_{n+1}=s_{n}{}^{2}-2$$ |

for $n\ge 1$.

Title | Lucas-Lehmer primality test |
---|---|

Canonical name | LucasLehmerPrimalityTest |

Date of creation | 2013-03-22 14:24:31 |

Last modified on | 2013-03-22 14:24:31 |

Owner | CWoo (3771) |

Last modified by | CWoo (3771) |

Numerical id | 8 |

Author | CWoo (3771) |

Entry type | Theorem |

Classification | msc 11A51 |