# (26371^{13681} - 1)/26370

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.

#### This prime's information:

Description: | (26371^{13681} - 1)/26370 |
---|---|

Verification status (*): | PRP |

Official Comment (*): | Generalized repunit |

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

Proof-code(s): (*): | p170 : Wu_T, Primo, OpenPFGW |

Decimal Digits: | 60482 (log_{10} is 60481.011887298) |

Rank (*): | 57215 (digit rank is 1) |

Entrance Rank (*): | 31809 |

Currently on list? (*): | short |

Submitted: | 2/16/2012 07:33:47 UTC |

Last modified: | 3/11/2023 15:54:10 UTC |

Database id: | 104672 |

Status Flags: | Verify |

Score (*): | 38.0041 (normalized score 0.0008) |

#### 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.

- Generalized Repunit (archivable *)
- Prime on list:
yes, rank12

Subcategory: "Generalized Repunit"

(archival tag id 214045, tag last modified 2024-02-26 02:37:04)

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

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#### 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 104672 person_id 9 machine Ditto P4 P4 what trial_divided notes Command: /home/ditto/client/pfgw -o -f -q"(26371^13681-1)/26370" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] (26371^13681-1)/26370 1/1 mro=0 trial factoring to 19909641 (26371^13681-1)/26370 has no small factor. [Elapsed time: 95.478 seconds] modified 2020-07-07 22:30:28 created 2012-02-16 07:35:07 id 138933

field value prime_id 104672 person_id 9 machine Ditto P4 P4 what prp notes Command: /home/ditto/client/pfgw -tc -q"(26371^13681-1)/26370" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing (26371^13681-1)/26370 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 29 Running N+1 test using discriminant 67, base 3+sqrt(67) Calling N-1 BLS with factored part 0.48% and helper 0.00% (1.45% proof) (26371^13681-1)/26370 is Fermat and Lucas PRP! (1541.1355s+0.0037s) [Elapsed time: 25.68 minutes] modified 2020-07-07 22:30:28 created 2012-02-16 07:39:33 id 138935

Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.

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