# V(39607)/158429

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: | V(39607)/158429 |
---|---|

Verification status (*): | PRP |

Official Comment (*): | Lucas cofactor, ECPP |

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

Proof-code(s): (*): | c46 : Boncompagni, Primo |

Decimal Digits: | 8273 (log_{10} is 8272.1736326999) |

Rank (*): | 79596 (digit rank is 2) |

Entrance Rank (*): | 58211 |

Currently on list? (*): | short |

Submitted: | 12/23/2011 01:32:51 CDT |

Last modified: | 2/13/2012 10:20:26 CDT |

Database id: | 103784 |

Status Flags: | Verify |

Score (*): | 31.852 (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.

- Elliptic Curve Primality Proof (archivable *)
- Prime on list:
no, rank267

Subcategory: "ECPP"

(archival tag id 214042, tag last modified 2021-09-18 09:37:41)- Lucas cofactor (archivable *)
- Prime on list:
yes, rank16

Subcategory: "Lucas cofactor"

(archival tag id 214043, tag last modified 2020-09-11 12:20:26)

#### 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 103784 person_id 9 machine Ditto P4 P4 what trial_divided notes Command: /home/ditto/client/pfgw -o -f -q"V(39607)/158429" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] V(39607)/158429 1/1 mro=0 trial factoring to 2340388 V(39607)/158429 has no small factor. [Elapsed time: 1.788 seconds] modified 2020-07-07 17:30:29 created 2011-12-23 01:35:01 id 137157

field value prime_id 103784 person_id 9 machine Ditto P4 P4 what prp notes Command: /home/ditto/client/pfgw -tc -q"V(39607)/158429" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing V(39607)/158429 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 7 Running N+1 test using discriminant 13, base 6+sqrt(13) Calling N-1 BLS with factored part 0.17% and helper 0.06% (0.57% proof) V(39607)/158429 is Fermat and Lucas PRP! (29.2825s+0.0032s) [Elapsed time: 29.00 seconds] modified 2020-07-07 17:30:29 created 2011-12-23 01:38:02 id 137158

Query times: 0.0004 seconds to select prime, 0.0009 seconds to seek comments.

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