# p(140791396)

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: | p(140791396) |
---|---|

Verification status (*): | PRP |

Official Comment (*): | Partitions, ECPP |

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

Proof-code(s): (*): | E6 : Lasher, Broadhurst, Underwood, CM |

Decimal Digits: | 13210 (log_{10} is 13209.341474841) |

Rank (*): | 79646 (digit rank is 3) |

Entrance Rank (*): | 75522 |

Currently on list? (*): | short |

Submitted: | 7/11/2022 18:53:15 UTC |

Last modified: | 5/20/2023 20:59:19 UTC |

Database id: | 134145 |

Blob database id: | 420 |

Status Flags: | Verify |

Score (*): | 33.3024 (normalized score 0) |

#### Description: (from blob table id=420)

The number of unrestricted integer partitions of 140791396 is p(140791396).

#### 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, rank206

Subcategory: "ECPP"

(archival tag id 227212, tag last modified 2024-07-11 00:37:12)- Partitions (archivable *)
- Prime on list:
yes, rank20

Subcategory: "Partitions"

(archival tag id 227213, tag last modified 2023-03-11 15:53:59)

#### 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 134145 person_id 9 machine Using: Dual Intel Xeon Gold 5222 CPUs 3.8GHz what prp notes PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8]

Primality testing 2195121766...4025571551 [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 11

Running N+1 test using discriminant 17, base 1+sqrt(17)

Calling N+1 BLS with factored part 0.07% and helper 0.03% (0.25% proof)

2195121766...4025571551 is Fermat and Lucas PRP! (6.1350s+0.0008s)

[Elapsed time: 6.00 seconds]modified 2022-07-11 19:26:07 created 2022-07-11 19:26:01 id 179915

field value prime_id 134145 person_id 9 machine Using: Dual Intel Xeon Gold 5222 CPUs 3.8GHz what requested notes pfgw modified 2022-07-11 18:56:01 created 2022-07-11 18:56:01 id 179907

Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.

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