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# 2^{9941} - 1

At this site we maintain a list of the 5000 Largest Known Primes which is updated hourly. This list is the most important PrimePages database: a collection of research, records and results all about prime numbers. This page summarizes our information about one of these primes.

Description: | 2^{9941} - 1 |
---|---|

Verification status (*): | Proven |

Official Comment (*): | Mersenne 22 |

Proof-code(s): (*): | G : Gillies |

Decimal Digits: | 2993 (log_{10} is 2992.53918689564) |

Rank (*): | 90028 (digit rank is 1) |

Entrance Rank (*): | 1 |

Currently on list? (*): | no |

Submitted: | 5/16/1963 |

Last modified: | 0/0/0000 00:00:00 CDT |

Database id: | 29731 |

Status Flags: | none |

Score (*): | 28.6927 (normalized score 0) |

#### Archival tags:

There are certain forms classed as archivable: these prime may (at times) remain on this list even if they do not make the Top 5000 proper. Such primes are tracked with archival tags.

#### Verification data:

The Top 5000 Primes is a list for proven primes only. In order to maintain the integrity of this list, we seek to verify the primality of all submissions. We are currently unable to check all proofs (ECPP, KP, ...), but we will at least trial divide and PRP check every entry before it is included in the list.

field value prime_id 29731 person_id 9 machine Windows XP P4 1.8GHz what prime notes Primality testing 2^9941-1 [N+1, Brillhart-Lehmer-Selfridge] Calling Brillhart-Lehmer-Selfridge with factored part 100.01% 2^9941-1 is prime! (2.938000 seconds) PFGW Version 20021217.Win_Dev (Beta 'caveat utilitor') [FFT v22.7 w/P4] Running N+1 test using discriminant 3, base 1+sqrt(3) modified 2003-03-25 11:23:48 created 2002-12-27 14:56:20 id 53272

Query times: 0.0004 seconds to select prime, 0.0007 seconds to seek comments.

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