# p(322610098)

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(322610098) |
---|---|

Verification status (*): | PRP |

Official Comment (*): | Partitions, ECPP |

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

Proof-code(s): (*): | E1 : Batalov, CM |

Decimal Digits: | 20000 (log_{10} is 19999.749690972) |

Rank (*): | 69806 (digit rank is 2) |

Entrance Rank (*): | 69492 |

Currently on list? (*): | short |

Submitted: | 6/27/2022 19:53:40 CDT |

Last modified: | 7/11/2022 11:50:09 CDT |

Database id: | 134096 |

Blob database id: | 412 |

Status Flags: | Verify, TrialDiv |

Score (*): | 34.5862 (normalized score 0) |

#### Description: (from blob table id=412)

The number of unrestricted integer partitions of 322610098 is p(322610098).

#### 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, rank63

Subcategory: "ECPP"

(archival tag id 227182, tag last modified 2022-09-09 14:37:23)- Partitions (archivable *)
- Prime on list:
yes, rank6

Subcategory: "Partitions"

(archival tag id 227183, tag last modified 2022-08-02 14:37:22)

#### 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 134096 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 5619413257...2440863153 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 5 Running N+1 test using discriminant 11, base 1+sqrt(11) Calling N+1 BLS with factored part 0.08% and helper 0.01% (0.24% proof) 5619413257...2440863153 is Fermat and Lucas PRP! (10.2557s+0.0015s) [Elapsed time: 10.00 seconds] modified 2022-07-11 13:21:44 created 2022-07-11 11:48:00 id 179889

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

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