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# primV(7577, - 1, 10692)

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: | primV(7577, - 1, 10692) |
---|---|

Verification status (*): | PRP |

Official Comment (*): | Generalized Lucas primitive part |

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

Proof-code(s): (*): | x33 : Carmody, Broadhurst, Water, Renze, OpenPFGW, Primo |

Decimal Digits: | 25140 (log_{10} is 25139.142470395) |

Rank (*): | 69256 (digit rank is 2) |

Entrance Rank (*): | 22853 |

Currently on list? (*): | short |

Submitted: | 4/15/2007 20:39:14 UTC |

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

Database id: | 80038 |

Status Flags: | Verify |

Score (*): | 35.2934 (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 primitive part (archivable *)
- Prime on list:
yes, rank20

Subcategory: "Generalized Lucas primitive part"

(archival tag id 191786, 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 80038 person_id 9 machine RedHat P4 P4 what trial_divided notes Command: /home/caldwell/client/pfgw -o -f -q"primV(7577,-1,10692)" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] trial factoring to 7762304 primV(7577,-1,10692) has no small factor. [Elapsed time: 16.619 seconds] modified 2020-07-07 22:30:41 created 2007-04-15 20:52:01 id 89184

field value prime_id 80038 person_id 9 machine RedHat P4 P4 what prp notes Command: /home/caldwell/client/pfgw -tc -q"primV(7577,-1,10692)" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing primV(7577,-1,10692) [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 41 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(10240,21) to FFT(10240,20) Reduced from FFT(10240,20) to FFT(10240,19) Reduced from FFT(10240,19) to FFT(10240,18) Reduced from FFT(10240,18) to FFT(10240,17) 167030 bit request FFT size=(10240,17) Running N-1 test using base 61 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(10240,21) to FFT(10240,20) Reduced from FFT(10240,20) to FFT(10240,19) Reduced from FFT(10240,19) to FFT(10240,18) Reduced from FFT(10240,18) to FFT(10240,17) 167030 bit request FFT size=(10240,17) Running N+1 test using discriminant 71, base 23+sqrt(71) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(10240,21) to FFT(10240,20) Reduced from FFT(10240,20) to FFT(10240,19) Reduced from FFT(10240,19) to FFT(10240,18) Reduced from FFT(10240,18) to FFT(10240,17) 167038 bit request FFT size=(10240,17) Calling N-1 BLS with factored part 1.43% and helper 0.03% (4.31% proof) primV(7577,-1,10692) is Fermat and Lucas PRP! (359.4600s+0.1500s) [Elapsed time: 360 seconds] modified 2020-07-07 22:30:41 created 2007-04-15 21:22:41 id 89187

Query times: 0.0003 seconds to select prime, 0.0006 seconds to seek comments.

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