# E(676)/878618128969410121818976030235415670049335313139\

11504892717789158174298202475475590955674162377015

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: | E(676)/878618128969410121818976030235415670049335313139\ 11504892717789158174298202475475590955674162377015 |
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Verification status (*): | PRP |

Official Comment (*): | Euler irregular, ECPP |

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

Proof-code(s): (*): | c8 : Water, Broadhurst, Primo |

Decimal Digits: | 1391 (log_{10} is 1390.8590865956) |

Rank (*): | 104447 (digit rank is 2) |

Entrance Rank (*): | 86383 |

Currently on list? (*): | no |

Submitted: | 2/16/2013 06:49:59 CDT |

Last modified: | 2/16/2013 07:50:27 CDT |

Database id: | 111255 |

Blob database id: | 293 |

Status Flags: | Verify |

Score (*): | 26.3034 (normalized score 0) |

#### title='from prime_blob table' id='blob'>Description: (from blob table id=293)

[This prime has a pre-calculated decimal expansion (linked blob)]

#### 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.

- Euler Irregular primes (archivable *)
- Prime on list:
no, rank22

Subcategory: "Euler Irregular primes"

(archival tag id 215081, tag last modified 2020-12-26 21:50:12)- Elliptic Curve Primality Proof (archivable *)
- Prime on list:
no, rank883

Subcategory: "ECPP"

(archival tag id 215082, tag last modified 2021-01-04 08:20:12)

#### 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 111255 person_id 9 machine RedHat P4 P4 what trial_divided notes PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] 7229139337343211....2702518970625923 1/1 mro=0 trial factoring to 335831 7229139337...8970625923 has no small factor. [Elapsed time: 0.325 seconds] modified 2020-07-07 17:30:22 created 2013-02-16 06:52:02 id 152780

field value prime_id 111255 person_id 9 machine Ditto P4 P4 what prp notes PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing 7229139337...8970625923 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Running N+1 test using discriminant 5, base 1+sqrt(5) Calling N+1 BLS with factored part 0.37% and helper 0.02% (1.17% proof) 7229139337...8970625923 is Fermat and Lucas PRP! (0.6130s+0.0005s) [Elapsed time: 1.00 seconds] modified 2020-07-07 17:30:22 created 2013-02-16 07:23:13 id 152783

Query times: 0.0005 seconds to select prime, 0.0007 seconds to seek comments.

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