# (2^{41521} - 1)/41602235382028197528613357724450752065089

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.

#### This prime's information:

Description: | (2^{41521} - 1)/41602235382028197528613357724450752065089 |
---|---|

Verification status (*): | PRP |

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

Proof-code(s): (*): | c54 : Wu_T, Primo |

Decimal Digits: | 12459 (log_{10} is 12458.447333297) |

Rank (*): | 76828 (digit rank is 2) |

Entrance Rank (*): | 58448 |

Currently on list? (*): | short |

Submitted: | 8/21/2012 00:57:18 CDT |

Last modified: | 8/21/2012 01:50:26 CDT |

Database id: | 108899 |

Status Flags: | Verify |

Score (*): | 33.1212 (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, rank202

Subcategory: "ECPP"

(archival tag id 214461, tag last modified 2022-11-14 11:36:29)- Mersenne cofactor (archivable *)
- Prime on list:
yes, rank14

Subcategory: "Mersenne cofactor"

(archival tag id 214462, tag last modified 2022-11-14 11:36:30)

#### 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 108899 person_id 9 machine Ditto P4 P4 what trial_divided notes Command: /home/ditto/client/pfgw -o -f -q"(2^41521-1)/41602235382028197528613357724450752065089" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] (2^41521-1)/4160....7724450752065089 1/1 mro=0 trial factoring to 3643482 (2^41521-1)/4160223538...0752065089 has no small factor. [Elapsed time: 5.291 seconds] modified 2020-07-07 17:30:24 created 2012-08-21 01:05:02 id 147381

field value prime_id 108899 person_id 9 machine Ditto P4 P4 what prp notes Command: /home/ditto/client/pfgw -tc -q"(2^41521-1)/41602235382028197528613357724450752065089" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing (2^41521-1)/4160223538...0752065089 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 11 Running N+1 test using discriminant 41, base 1+sqrt(41) Calling N-1 BLS with factored part 0.09% and helper 0.05% (0.33% proof) (2^41521-1)/4160223538...0752065089 is Fermat and Lucas PRP! (58.9730s+0.0004s) [Elapsed time: 59.00 seconds] modified 2020-07-07 17:30:24 created 2012-08-21 01:43:38 id 147382

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

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