# 2840178 · Bern(1870)/85

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: | 2840178 · Bern(1870)/85 |
---|---|

Verification status (*): | PRP |

Official Comment (*): | Irregular, ECPP |

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

Decimal Digits: | 3821 (log_{10} is 3820.47675595) |

Rank (*): | 88610 (digit rank is 1) |

Entrance Rank (*): | 32314 |

Currently on list? (*): | short |

Submitted: | 12/2/2003 20:49:03 CDT |

Last modified: | 12/2/2003 20:49:03 CDT |

Database id: | 67526 |

Status Flags: | Verify |

Score (*): | 29.4528 (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, rank19

Subcategory: "Irregular Primes"

(archival tag id 178452, tag last modified 2021-05-01 12:20:47)- Elliptic Curve Primality Proof (archivable *)
- Prime on list:
no, rank546

Subcategory: "ECPP"

(archival tag id 178453, tag last modified 2021-06-15 13:07:45)

#### 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 67526 person_id 9 machine Linux P4 2.8GHz what prp notes PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 2997477656...5776579313 [N-1/N+1, Brillhart-Lehmer-Selfridge] trial factoring to 1012270 Running N-1 test using base 3 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(1536,21) to FFT(1536,20) Reduced from FFT(1536,20) to FFT(1536,19) Reduced from FFT(1536,19) to FFT(1536,18) Reduced from FFT(1536,18) to FFT(1536,17) 25392 bit request FFT size=(1536,17) Running N+1 test using discriminant 11, base 1+sqrt(11) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(1536,21) to FFT(1536,20) Reduced from FFT(1536,20) to FFT(1536,19) Reduced from FFT(1536,19) to FFT(1536,18) Reduced from FFT(1536,18) to FFT(1536,17) 25400 bit request FFT size=(1536,17) Calling N+1 BLS with factored part 0.23% and helper 0.09% (0.77% proof) 2997477656...5776579313 is Fermat and Lucas PRP! (11.0226s+0.0018s) modified 2020-07-07 17:30:47 created 2003-12-02 20:53:02 id 72462

Query times: 0.0004 seconds to select prime, 0.0007 seconds to seek comments.

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