# double Mersenne number

A double Mersenne number is a number of the form ${2}^{{2}^{p}-1}-1$. Put another way, negative one plus 2 raised to the power of a Mersenne number. The first few double Mersenne numbers (and the ones small enough to show here) are: 3, 7, 127, 170141183460469231731687303715884105727.

If a double Mersenne number is itself prime, then it is called a double Mersenne prime. Obviously its index is then a Mersenne prime. The four double Mersenne numbers listed above are all primes, but as of today, ${2}^{170141183460469231731687303715884105727}-1$ is a probable prime^{}, despite an intense effort to find factors. (According to the Prime Pages, if it’s composite, its least prime factor^{} must be at least $5\times {10}^{51}$.

Title | double Mersenne number |
---|---|

Canonical name | DoubleMersenneNumber |

Date of creation | 2013-03-22 17:38:50 |

Last modified on | 2013-03-22 17:38:50 |

Owner | PrimeFan (13766) |

Last modified by | PrimeFan (13766) |

Numerical id | 4 |

Author | PrimeFan (13766) |

Entry type | Definition |

Classification | msc 11A41 |