# primV(57724)

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: | primV(57724) |
---|---|

Verification status (*): | PRP |

Official Comment (*): | Lucas primitive part, cyclotomy |

Unofficial Comments: | This prime has 1 user comment below. |

Proof-code(s): (*): | p54 : Broadhurst, Water, OpenPFGW |

Decimal Digits: | 12063 (log_{10} is 12062.75744775) |

Rank (*): | 76033 (digit rank is 3) |

Entrance Rank (*): | 12870 |

Currently on list? (*): | short |

Submitted: | 7/23/2001 22:15:40 CDT |

Last modified: | 7/23/2001 22:15:40 CDT |

Database id: | 16123 |

Status Flags: | Verify |

Score (*): | 33.0212 (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.

- Cyclotomy Proof (tolerated *)
- Prime on list:
no, rank36

Subcategory: "Cyclotomy Proof"

(archival tag id 193900, tag last modified 2019-06-27 21:50:21)- Lucas primitive part (archivable *)
- Prime on list:
yes, rank15

Subcategory: "Lucas primitive part"

(archival tag id 195656, tag last modified 2021-02-13 15:20:13)

#### User comments about this prime (disclaimer):

User comments are allowed to convey mathematical information about this number, how it was proven prime.... See our guidelines and restrictions.

#### 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 16123 person_id 9 machine Linux PII 200 what prp notes PFGW Version 20020311.x86_Dev (Alpha software, 'caveat utilitor') Primality Running N-1 test using base 7 6467965237...1981256401 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 13 Running N+1 test using discriminant 19, base 15+sqrt(19) Calling N-1 BLS with factored part 1.88% and helper 0.44% (6.07% proof) primV(57724) is Fermat and Lucas PRP! (-1295.227296 seconds) modified 2003-03-25 11:22:39 created 2003-01-09 19:59:11 id 64967

Query times: 0.0005 seconds to select prime, 0.0007 seconds to seek comments.

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