# (2^{63703} - 1)/42808417

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: | (2^{63703} - 1)/42808417 |
---|---|

Verification status (*): | PRP |

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

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

Proof-code(s): (*): | c59 : Metcalfe, OpenPFGW, Primo |

Decimal Digits: | 19169 (log_{10} is 19168.882284614) |

Rank (*): | 69420 (digit rank is 1) |

Entrance Rank (*): | 58136 |

Currently on list? (*): | short |

Submitted: | 1/9/2014 13:21:24 CDT |

Last modified: | 1/9/2014 13:51:04 CDT |

Database id: | 116871 |

Status Flags: | Verify, TrialDiv |

Score (*): | 34.455 (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, rank41

Subcategory: "ECPP"

(archival tag id 217568, tag last modified 2021-09-18 09:37:41)- Mersenne cofactor (archivable *)
- Prime on list:
yes, rank3

Subcategory: "Mersenne cofactor"

(archival tag id 217569, tag last modified 2021-02-24 00:50:28)

#### 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 116871 person_id 9 machine RedHat P4 P4 what prp notes Command: /home/caldwell/client/pfgw -tc -q"(2^63703-1)/42808417" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing (2^63703-1)/42808417 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Running N-1 test using base 7 Running N-1 test using base 13 Running N+1 test using discriminant 19, base 1+sqrt(19) Calling N-1 BLS with factored part 0.12% and helper 0.01% (0.36% proof) (2^63703-1)/42808417 is Fermat and Lucas PRP! (233.6976s+0.0004s) [Elapsed time: 3.90 minutes] modified 2020-07-07 17:30:18 created 2014-01-09 13:23:01 id 162380

Query times: 0.0002 seconds to select prime, 0.0028 seconds to seek comments.

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