# (V(561, 1, 6309) + 1)/(V(561, 1, 9) + 1)

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Description: | (V(561, 1, 6309) + 1)/(V(561, 1, 9) + 1) |
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Verification status (*): | PRP |

Official Comment (*): | Lehmer primitive part |

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

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

Decimal Digits: | 17319 (log_{10} is 17318.457332283) |

Rank (*): | 70648 (digit rank is 1) |

Entrance Rank (*): | 63819 |

Currently on list? (*): | short |

Submitted: | 5/6/2016 18:23:45 CDT |

Last modified: | 5/6/2016 18:50:18 CDT |

Database id: | 121624 |

Status Flags: | Verify, TrialDiv |

Score (*): | 34.1409 (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, rank11

Subcategory: "Lehmer primitive part"

(archival tag id 218329, tag last modified 2019-08-26 13:20:28)

#### 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 121624 person_id 9 machine Using: Xeon 4c+4c 3.5GHz what prp notes Command: /home/caldwell/client/pfgw/pfgw64 -tc -q"(lucasV(561,1,6309)+1)/(lucasV(561,1,9)+1)" 2>&1 PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing (lucasV(561,1,6309)+1)/(lucasV(561,1,9)+1) [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 37 Running N-1 test using base 47 Running N+1 test using discriminant 61, base 12+sqrt(61) Calling N-1 BLS with factored part 1.77% and helper 0.07% (5.38% proof) (lucasV(561,1,6309)+1)/(lucasV(561,1,9)+1) is Fermat and Lucas PRP! (28.0809s+0.2187s) [Elapsed time: 28.00 seconds] modified 2020-07-07 17:30:16 created 2016-05-06 18:31:01 id 167262

Query times: 0.0002 seconds to select prime, 0.0006 seconds to seek comments.

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