# U(11200, - 1, 5039)

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#### This prime's information:

Description: | U(11200, - 1, 5039) |
---|---|

Verification status (*): | PRP |

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

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

Proof-code(s): (*): | x25 : Broadhurst, Water, OpenPFGW, Primo |

Decimal Digits: | 20400 (log_{10} is 20399.960415652) |

Rank (*): | 73515 (digit rank is 1) |

Entrance Rank (*): | 14936 |

Currently on list? (*): | short |

Submitted: | 3/9/2004 15:09:50 UTC |

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

Database id: | 69430 |

Status Flags: | Verify |

Score (*): | 34.6475 (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.

- Cyclotomy Proof (tolerated *)
- Prime on list:
no, rank10

Subcategory: "Cyclotomy Proof"

(archival tag id 192169, tag last modified 2023-03-11 15:53:59)- Generalized Lucas Number (archivable *)
- Prime on list:
yes, rank18

Subcategory: "Generalized Lucas Number"

(archival tag id 192168, 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 69430 person_id 9 machine Linux P4 2.8GHz what prp notes Command: /home/caldwell/client/pfgw -f -tc -q"lucasU(11200,-1,5039)" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing lucasU(11200,-1,5039) [N-1/N+1, Brillhart-Lehmer-Selfridge] trial factoring to 6199893 Running N-1 test using base 37 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) Reduced from FFT(8192,18) to FFT(8192,17) 135544 bit request FFT size=(8192,17) Running N-1 test using base 59 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) Reduced from FFT(8192,18) to FFT(8192,17) 135544 bit request FFT size=(8192,17) 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) Reduced from FFT(8192,18) to FFT(8192,17) 135544 bit request FFT size=(8192,17) Running N+1 test using discriminant 79, base 16+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) Reduced from FFT(8192,18) to FFT(8192,17) 135552 bit request FFT size=(8192,17) Calling N-1 BLS with factored part 1.24% and helper 0.26% (3.97% proof) lucasU(11200,-1,5039) is Fermat and Lucas PRP! (559.4009s+0.0258s) modified 2020-07-07 22:30:45 created 2004-03-09 15:23:00 id 74383

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

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