# primV(123573)

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.

Description: | primV(123573) |
---|---|

Verification status (*): | PRP |

Official Comment (*): | Lucas primitive part, ECPP |

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

Proof-code(s): (*): | c77 : Batalov, Primo |

Decimal Digits: | 16198 (log_{10} is 16197.562154611) |

Rank (*): | 71126 (digit rank is 1) |

Entrance Rank (*): | 68085 |

Currently on list? (*): | short |

Submitted: | 5/14/2019 21:45:07 CDT |

Last modified: | 5/14/2019 22:20:21 CDT |

Database id: | 126462 |

Status Flags: | Verify, TrialDiv |

Score (*): | 33.9338 (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.

- Lucas primitive part (archivable *)
- Prime on list:
yes, rank5

Subcategory: "Lucas primitive part"

(archival tag id 220257, tag last modified 2021-02-13 15:20:13)- Elliptic Curve Primality Proof (archivable *)
- Prime on list:
no, rank66

Subcategory: "ECPP"

(archival tag id 220258, tag last modified 2021-09-18 09:37:41)

#### 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 126462 person_id 9 machine Using: Xeon 4c+4c 3.5GHz what prp notes PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing 3648838243...8552986081 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 37 Running N-1 test using base 43 Running N-1 test using base 53 Running N+1 test using discriminant 67, base 14+sqrt(67) Calling N-1 BLS with factored part 0.32% and helper 0.07% (1.04% proof) 3648838243...8552986081 is Fermat and Lucas PRP! (30.6440s+0.0019s) [Elapsed time: 30.00 seconds] modified 2020-07-07 17:30:13 created 2019-05-14 21:51:02 id 172148

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

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