# (U(9275, 1, 3961) + U(9275, 1, 3960))/(U(9275, 1, 45) + U(9275, 1, 44))

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#### This prime's information:

Description: | (U(9275, 1, 3961) + U(9275, 1, 3960))/(U(9275, 1, 45) + U(9275, 1, 44)) |
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Verification status (*): | PRP |

Official Comment (*): | Lehmer primitive part |

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

Proof-code(s): (*): | x38 : Broadhurst, OpenPFGW, Primo |

Decimal Digits: | 15537 (log_{10} is 15536.001284243) |

Rank (*): | 77109 (digit rank is 2) |

Entrance Rank (*): | 35575 |

Currently on list? (*): | short |

Submitted: | 5/10/2009 09:19:03 UTC |

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

Database id: | 88162 |

Status Flags: | Verify |

Score (*): | 33.8047 (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.

- Lehmer primitive part (archivable *)
- Prime on list:
yes, rank20

Subcategory: "Lehmer primitive part"

(archival tag id 210442, tag last modified 2023-03-11 15:53:59)

#### 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 88162 person_id 9 machine RedHat P4 P4 what prp notes Command: /home/caldwell/client/pfgw -tc -q"(lucasU(9275,1,3961)+lucasU(9275,1,3960))/(lucasU(9275,1,45)+lucasU(9275,1,44))" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing (lucasU(9275,1,3961)+lucasU(9275,1,3960))/(lucasU(9275,1,45)+lucasU(9275,1,44)) [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(6144,21) to FFT(6144,20) Reduced from FFT(6144,20) to FFT(6144,19) Reduced from FFT(6144,19) to FFT(6144,18) Reduced from FFT(6144,18) to FFT(6144,17) 103228 bit request FFT size=(6144,17) Running N-1 test using base 7 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(6144,21) to FFT(6144,20) Reduced from FFT(6144,20) to FFT(6144,19) Reduced from FFT(6144,19) to FFT(6144,18) Reduced from FFT(6144,18) to FFT(6144,17) 103228 bit request FFT size=(6144,17) Running N+1 test using discriminant 23, base 1+sqrt(23) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(6144,21) to FFT(6144,20) Reduced from FFT(6144,20) to FFT(6144,19) Reduced from FFT(6144,19) to FFT(6144,18) Reduced from FFT(6144,18) to FFT(6144,17) 103236 bit request FFT size=(6144,17) Calling N-1 BLS with factored part 0.57% and helper 0.29% (2.01% proof) (lucasU(9275,1,3961)+lucasU(9275,1,3960))/(lucasU(9275,1,45)+lucasU(9275,1,44)) is Fermat and Lucas PRP! (150.4400s+0.0100s) [Elapsed time: 2.77 minutes] modified 2020-07-07 22:30:38 created 2009-05-10 09:23:01 id 105686

field value prime_id 88162 person_id 9 machine Ditto P4 P4 what trial_divided notes Command: /home/ditto/client/pfgw -o -f -q"(lucasU(9275,1,3961)+lucasU(9275,1,3960))/(lucasU(9275,1,45)+lucasU(9275,1,44))" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] (lucasU(9275,1,3961)+luca.........,1,45)+lucasU(92 1/1 trial factoring to 4623227 (lucasU(9275,1,3961)+lucasU(9275,1,3960))/(lucasU(9275,1,45)+lucasU(9275,1,44)) has no small factor. [Elapsed time: 6.252 seconds] modified 2020-07-07 22:30:38 created 2009-05-10 09:35:01 id 105687

Query times: 0.0007 seconds to select prime, 0.0005 seconds to seek comments.

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