# 48047305725 · 2^{172403} - 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: | 48047305725 · 2^{172403} - 1 |
---|---|

Verification status (*): | Proven |

Official Comment (*): | Sophie Germain (p) |

Proof-code(s): (*): | L99 : Underbakke, TwinGen, LLR |

Decimal Digits: | 51910 (log_{10} is 51909.156011497) |

Rank (*): | 55305 (digit rank is 2) |

Entrance Rank (*): | 11525 |

Currently on list? (*): | short |

Submitted: | 1/25/2007 08:21:41 CDT |

Last modified: | 1/25/2007 08:56:33 CDT |

Database id: | 79261 |

Status Flags: | none |

Score (*): | 37.5326 (normalized score 0.001) |

#### 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.

- Sophie Germain (p) (archivable *)
- Prime on list:
yes, rank9

Subcategory: "Sophie Germain (p)"

(archival tag id 189914, tag last modified 2020-05-17 15:50:28)

#### 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 79261 person_id 9 machine RedHat P4 P4 what trial_divided notes Command: /home/caldwell/client/TrialDiv/TrialDiv -q 48047305725 2 172403 -1 2>&1 [Elapsed time: 9.178 seconds] modified 2020-07-07 17:30:42 created 2007-01-25 08:22:11 id 87629

field value prime_id 79261 person_id 9 machine RedHat P4 P4 what prime notes Command: /home/caldwell/client/llr.pl 48047305725*2^172403-1 2>&1 Starting Lucas Lehmer Riesel prime test of 48047305725*2^172403-1 V1 = 5 ; Computing U0... Done Computing U0. Starting Lucas-Lehmer loop... 48047305725*2^172403-1 is prime! Time: 262.491 sec. [Elapsed time: 262 seconds] modified 2020-07-07 17:30:42 created 2007-01-25 08:52:11 id 87631

Query times: 0.0004 seconds to select prime, 0.0006 seconds to seek comments.

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