# "10000000000000000000...(34053 other digits)...00000000000000532669"

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: | "10000000000000000000...(34053 other digits)...00000000000000532669" |
---|---|

Verification status (*): | PRP |

Official Comment (*): | ECPP |

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

Proof-code(s): (*): | c84 : Underwood, Primo |

Decimal Digits: | 34093 (log_{10} is 34092) |

Rank (*): | 65822 (digit rank is 1) |

Entrance Rank (*): | 55240 |

Currently on list? (*): | no |

Submitted: | 11/23/2016 14:03:47 UTC |

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

Database id: | 122527 |

Blob database id: | 359 |

Status Flags: | Verify |

Score (*): | 36.2347 (normalized score 0.0001) |

#### Description: (from blob table id=359)

Arranged in a 103 by 331 grid this prime depicts the Mersenne prime exponent 57,885,161

#### 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, rank27

Subcategory: "ECPP"

(archival tag id 218523, tag last modified 2023-12-16 03:37:30)

#### 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 122527 person_id 9 machine Using: Xeon 4c+4c 3.5GHz what prp notes Command: /home/caldwell/client/pfgw/pfgw64 -tc p_122527.txt 2>&1 PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing 1000000000...0000532669 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Running N+1 test using discriminant 7, base 2+sqrt(7) Calling N+1 BLS with factored part 0.05% and helper 0.02% (0.15% proof) 1000000000...0000532669 is Fermat and Lucas PRP! (92.2635s+0.0162s) [Elapsed time: 1.53 minutes] modified 2020-07-07 22:30:16 created 2016-11-23 14:11:02 id 168168

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

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