# V(52201)/705\

85804042896975505694709575919458733851279868446609

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(52201)/705\ 85804042896975505694709575919458733851279868446609 |
---|---|

Verification status (*): | PRP |

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

Proof-code(s): (*): | c8 : Broadhurst, Water, Primo |

Decimal Digits: | 10857 (log_{10} is 10856.515091323) |

Rank (*): | 76975 (digit rank is 1) |

Entrance Rank (*): | 68139 |

Currently on list? (*): | short |

Submitted: | 3/12/2015 15:52:56 CDT |

Last modified: | 3/12/2015 17:20:30 CDT |

Database id: | 119540 |

Status Flags: | Verify, TrialDiv |

Score (*): | 32.6948 (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, rank167

Subcategory: "ECPP"

(archival tag id 217919, tag last modified 2021-09-18 09:37:41)- Lucas cofactor (archivable *)
- Prime on list:
yes, rank7

Subcategory: "Lucas cofactor"

(archival tag id 217920, tag last modified 2020-09-11 12:20:26)

#### 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 119540 person_id 9 machine Using: Xeon 4c+4c 3.5GHz what prp notes Command: /home/caldwell/client/pfgw/pfgw64 -tc -q"V(52201)/70585804042896975505694709575919458733851279868446609" 2>&1 PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing V(52201)/7058580404...9868446609 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Running N+1 test using discriminant 7, base 1+sqrt(7) Calling N-1 BLS with factored part 0.07% and helper 0.02% (0.23% proof) V(52201)/7058580404...9868446609 is Fermat and Lucas PRP! (8.0725s+0.0008s) [Elapsed time: 8.00 seconds] modified 2020-07-07 17:30:17 created 2015-03-12 17:00:31 id 165149

Query times: 0.0003 seconds to select prime, 0.0004 seconds to seek comments.

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