# U(19258, - 1, 5039)

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(19258, - 1, 5039) |
---|---|

Verification status (*): | PRP |

Official Comment (*): | Generalized Lucas number |

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

Proof-code(s): (*): | x23 : Broadhurst, Water, Renze, OpenPFGW, Primo |

Decimal Digits: | 21586 (log_{10} is 21585.871142678) |

Rank (*): | 73146 (digit rank is 1) |

Entrance Rank (*): | 24366 |

Currently on list? (*): | short |

Submitted: | 4/22/2007 18:04:14 UTC |

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

Database id: | 80154 |

Status Flags: | Verify |

Score (*): | 34.8223 (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, rank17

Subcategory: "Generalized Lucas Number"

(archival tag id 192115, tag last modified 2023-10-24 02:37:13)

#### 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 80154 person_id 9 machine RedHat P4 P4 what trial_divided notes Command: /home/caldwell/client/pfgw -o -f -q"lucasU(19258,-1,5039)" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] lucas trial factoring to 6588625 lucasU(19258,-1,5039) has no small factor. [Elapsed time: 12.123 seconds] modified 2020-07-07 22:30:41 created 2007-04-22 18:22:01 id 89417

field value prime_id 80154 person_id 9 machine RedHat P4 P4 what prp notes Command: /home/caldwell/client/pfgw -tc -q"lucasU(19258,-1,5039)" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing lucasU(19258,-1,5039) [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 53 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(8192,21) to FFT(8192,20) Reduced from FFT(8192,20) to FFT(8192,19) Reduced from FFT(8192,19) to FFT(8192,18) 143422 bit request FFT size=(8192,18) Running N-1 test using base 61 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(8192,21) to FFT(8192,20) Reduced from FFT(8192,20) to FFT(8192,19) Reduced from FFT(8192,19) to FFT(8192,18) 143422 bit request FFT size=(8192,18) Running N-1 test using base 67 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(8192,21) to FFT(8192,20) Reduced from FFT(8192,20) to FFT(8192,19) Reduced from FFT(8192,19) to FFT(8192,18) 143422 bit request FFT size=(8192,18) Running N+1 test using discriminant 79, base 20+sqrt(79) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(8192,21) to FFT(8192,20) Reduced from FFT(8192,20) to FFT(8192,19) Reduced from FFT(8192,19) to FFT(8192,18) 143430 bit request FFT size=(8192,18) Calling N-1 BLS with factored part 1.24% and helper 0.48% (4.21% proof) lucasU(19258,-1,5039) is Fermat and Lucas PRP! (294.8400s+0.0100s) [Elapsed time: 295 seconds] modified 2020-07-07 22:30:41 created 2007-04-22 18:23:02 id 89418

Query times: 0.0003 seconds to select prime, 0.0008 seconds to seek comments.

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