# 31 · 2^{44653} - 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: | 31 · 2^{44653} - 1 |
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Verification status (*): | Proven |

Official Comment (*): | [none] |

Proof-code(s): (*): | g199 : Carmody, Proth.exe |

Decimal Digits: | 13444 (log_{10} is 13443.3837580776) |

Rank (*): | 73199 (digit rank is 1) |

Entrance Rank (*): | 4133 |

Currently on list? (*): | no |

Submitted: | 5/22/2000 05:42:01 CDT |

Last modified: | 5/22/2000 05:42:01 CDT |

Removed (*): | 7/1/2000 |

Database id: | 14061 |

Status Flags: | none |

Score (*): | 33.3568 (normalized score 0) |

#### 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 14061 person_id 9 machine Windows XP P4 1.8GHz what prime notes Primality testing 31*2^44653-1 [N+1, Brillhart-Lehmer-Selfridge] Calling Brillhart-Lehmer-Selfridge with factored part 99.99% 31*2^44653-1 is prime! (69.891000 seconds) PFGW Version 1.1 for Windows Running N+1 test using discriminant 3, base 1+sqrt(3) modified 2003-03-25 11:25:21 created 2002-12-10 03:40:40 id 36082

Query times: 0.0004 seconds to select prime, 0.0013 seconds to seek comments.

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