# 6 · Bern(4306)/2153

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: | 6 · Bern(4306)/2153 |
---|---|

Verification status (*): | PRP |

Official Comment (*): | Irregular, ECPP |

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

Proof-code(s): (*): | FE8 : Oakes, Broadhurst, Water, Morain, FastECPP |

Decimal Digits: | 10342 (log_{10} is 10341.250474092) |

Rank (*): | 78501 (digit rank is 1) |

Entrance Rank (*): | 40519 |

Currently on list? (*): | short |

Submitted: | 4/4/2009 12:16:15 CDT |

Last modified: | 4/4/2009 12:50:40 CDT |

Database id: | 87451 |

Status Flags: | Verify |

Score (*): | 32.5441 (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.

- Irregular Primes (archivable *)
- Prime on list:
yes, rank9

Subcategory: "Irregular Primes"

(archival tag id 208962, tag last modified 2021-05-01 12:20:47)- Elliptic Curve Primality Proof (archivable *)
- Prime on list:
no, rank209

Subcategory: "ECPP"

(archival tag id 208963, tag last modified 2022-05-17 18:37:30)

#### User comments about this prime (disclaimer):

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#### 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 87451 person_id 9 machine RedHat P4 P4 what trial_divided notes PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] 1780221704...9703946799.........1062015654039575 1/1 trial factoring to 2979440 1780221704...5593370631 has no small factor. [Elapsed time: 12.441 seconds] modified 2020-07-07 17:30:38 created 2009-04-04 12:18:13 id 104267

field value prime_id 87451 person_id 9 machine Ditto P4 P4 what prp notes PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 1780221704...5593370631 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 7 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(4096,21) to FFT(4096,20) Reduced from FFT(4096,20) to FFT(4096,19) Reduced from FFT(4096,19) to FFT(4096,18) Reduced from FFT(4096,18) to FFT(4096,17) 68714 bit request FFT size=(4096,17) Running N+1 test using discriminant 13, base 1+sqrt(13) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(4096,21) to FFT(4096,20) Reduced from FFT(4096,20) to FFT(4096,19) Reduced from FFT(4096,19) to FFT(4096,18) Reduced from FFT(4096,18) to FFT(4096,17) 68722 bit request FFT size=(4096,17) Calling N+1 BLS with factored part 0.10% and helper 0.09% (0.41% proof) 1780221704...5593370631 is Fermat and Lucas PRP! (46.5600s+0.0100s) [Elapsed time: 47.00 seconds] modified 2020-07-07 17:30:38 created 2009-04-04 12:46:28 id 104270

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

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