# 648621027630345 · 2^{253824} - 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: | 648621027630345 · 2^{253824} - 1 |
---|---|

Verification status (*): | Proven |

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

Proof-code(s): (*): | x24 : Jarai_Z, Farkas, Csajbok, Kasza, Jarai, Unknown |

Decimal Digits: | 76424 (log_{10} is 76423.449610438) |

Rank (*): | 48641 (digit rank is 3) |

Entrance Rank (*): | 16313 |

Currently on list? (*): | short |

Submitted: | 11/18/2009 12:17:18 CDT |

Last modified: | 11/18/2009 16:20:03 CDT |

Database id: | 90907 |

Status Flags: | none |

Score (*): | 38.7256 (normalized score 0.0035) |

#### 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, rank4

Subcategory: "Sophie Germain (p)"

(archival tag id 210551, tag last modified 2016-02-29 09:24:40)

#### 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 90907 person_id 9 machine RedHat P4 P4 what trial_divided notes Command: /home/caldwell/client/TrialDiv/TrialDiv -q 648621027630345 2 253824 -1 2>&1 [Elapsed time: 9.178 seconds] modified 2020-07-07 17:30:36 created 2009-11-18 12:18:11 id 111190

field value prime_id 90907 person_id 9 machine RedHat P4 P4 what prime notes Command: /home/caldwell/client/llr.pl 648621027630345*2^253824-1 2>&1 Starting Lucas Lehmer Riesel prime test of 648621027630345*2^253824-1 Using Zero Padded IBDWT : Mersenne fftlen = 12288, Used fftlen = 24576 V1 = 11 ; Computing U0... V1 = 11 ; Computing U0...done. Starting Lucas-Lehmer loop... 648621027630345*2^253824-1 is prime! Time : 174.569 sec. [Elapsed time: 2.90 minutes] modified 2020-07-07 17:30:36 created 2009-11-18 12:25:57 id 111192

Query times: 0.0004 seconds to select prime, 0.0003 seconds to seek comments.

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