# (2^{32531} - 1)/(65063 · 25225122959)

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^{32531} - 1)/(65063 · 25225122959) |
---|---|

Verification status (*): | PRP |

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

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

Proof-code(s): (*): | c60 : Lemsafer, Primo |

Decimal Digits: | 9778 (log_{10} is 9777.5916215688) |

Rank (*): | 78076 (digit rank is 2) |

Entrance Rank (*): | 61733 |

Currently on list? (*): | short |

Submitted: | 9/29/2012 00:54:59 CDT |

Last modified: | 9/29/2012 01:20:47 CDT |

Database id: | 109452 |

Status Flags: | Verify |

Score (*): | 32.3704 (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, rank228

Subcategory: "ECPP"

(archival tag id 214532, tag last modified 2021-09-18 09:37:41)- Mersenne cofactor (archivable *)
- Prime on list:
yes, rank12

Subcategory: "Mersenne cofactor"

(archival tag id 214533, tag last modified 2021-02-24 00:50:28)

#### 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 109452 person_id 9 machine Ditto P4 P4 what trial_divided notes Command: /home/ditto/client/pfgw -o -f -q"(2^32531-1)/(65063*25225122959)" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] (2^32531-1)/(65063*25225122959) 1/1 mro=0 trial factoring to 2804337 (2^32531-1)/(65063*25225122959) has no small factor. [Elapsed time: 2.502 seconds] modified 2020-07-07 17:30:24 created 2012-09-29 01:05:01 id 148553

field value prime_id 109452 person_id 9 machine Ditto P4 P4 what prp notes Command: /home/ditto/client/pfgw -tc -q"(2^32531-1)/(65063*25225122959)" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing (2^32531-1)/(65063*25225122959) [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Running N+1 test using discriminant 7, base 8+sqrt(7) Calling N-1 BLS with factored part 0.08% and helper 0.08% (0.33% proof) (2^32531-1)/(65063*25225122959) is Fermat and Lucas PRP! (43.0175s+0.0003s) [Elapsed time: 43.00 seconds] modified 2020-07-07 17:30:24 created 2012-09-29 01:08:01 id 148554

Query times: 0.0005 seconds to select prime, 0.0013 seconds to seek comments.

Printed from the PrimePages <primes.utm.edu> © Chris Caldwell.