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# U(5768, - 5769, 4591)

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: | U(5768, - 5769, 4591) |
---|---|

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: | 17264 (log_{10} is 17263.451398544) |

Rank (*): | 73648 (digit rank is 1) |

Entrance Rank (*): | 66967 |

Currently on list? (*): | short |

Submitted: | 11/8/2018 10:06:59 UTC |

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

Database id: | 125770 |

Status Flags: | Verify, TrialDiv |

Score (*): | 34.131 (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.

- Generalized Lucas Number (archivable *)
- Prime on list:
yes, rank20

Subcategory: "Generalized Lucas Number"

(archival tag id 219965, tag last modified 2023-03-11 16:02:31)- Cyclotomy Proof (tolerated *)
- Prime on list:
no, rank14

Subcategory: "Cyclotomy Proof"

(archival tag id 219966, tag last modified 2023-03-11 15:53:59)

#### 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 125770 person_id 9 machine Using: Xeon 4c+4c 3.5GHz what prp notes Command: /home/caldwell/client/pfgw/pfgw64 -tc -q"lucasU(5768,-5769,4591)" 2>&1 PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing lucasU(5768,-5769,4591) [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 17 Running N-1 test using base 29 Running N-1 test using base 47 Running N-1 test using base 83 Running N+1 test using discriminant 101, base 4+sqrt(101) Calling N-1 BLS with factored part 0.92% and helper 0.02% (2.80% proof) lucasU(5768,-5769,4591) is Fermat and Lucas PRP! (37.0425s+0.0022s) [Elapsed time: 37.00 seconds] modified 2020-07-07 22:30:14 created 2018-11-08 10:11:01 id 171447

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

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