# U(21041, - 1, 9059)

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: | U(21041, - 1, 9059) |
---|---|

Verification status (*): | PRP |

Official Comment (*): | Generalized Lucas number, cyclotomy |

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

Proof-code(s): (*): | x45 : Batalov, OpenPFGW, Primo, Unknown |

Decimal Digits: | 39159 (log_{10} is 39158.33524599) |

Rank (*): | 60022 (digit rank is 1) |

Entrance Rank (*): | 56432 |

Currently on list? (*): | short |

Submitted: | 11/20/2018 20:49:28 CDT |

Last modified: | 11/20/2018 21:20:24 CDT |

Database id: | 125803 |

Status Flags: | Verify, TrialDiv |

Score (*): | 36.6626 (normalized score 0.0004) |

#### 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 Lucas Number (archivable *)
- Prime on list:
yes, rank4

Subcategory: "Generalized Lucas Number"

(archival tag id 219985, tag last modified 2020-05-28 13:20:28)- Cyclotomy Proof (tolerated *)
- Prime on list:
no, rank2

Subcategory: "Cyclotomy Proof"

(archival tag id 219986, tag last modified 2018-11-21 18:50:17)

#### 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 125803 person_id 9 machine Using: Xeon 4c+4c 3.5GHz what prp notes Command: /home/caldwell/client/pfgw/pfgw64 -tc -q"lucasU(21041,-1,9059)" 2>&1 PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing lucasU(21041,-1,9059) [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Running N+1 test using discriminant 11, base 7+sqrt(11) Calling N-1 BLS with factored part 0.20% and helper 0.07% (0.67% proof) lucasU(21041,-1,9059) is Fermat and Lucas PRP! (138.6943s+0.0034s) [Elapsed time: 2.32 minutes] modified 2020-07-07 17:30:14 created 2018-11-20 20:51:01 id 171480

Query times: 0.0005 seconds to select prime, 0.001 seconds to seek comments.

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