# primV(27655, 1, 19926)

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: | primV(27655, 1, 19926) |
---|---|

Verification status (*): | PRP |

Official Comment (*): | Generalized Lucas primitive part |

Proof-code(s): (*): | x25 : Broadhurst, Water, OpenPFGW, Primo |

Decimal Digits: | 57566 (log_{10} is 57565.386662596) |

Rank (*): | 55518 (digit rank is 1) |

Entrance Rank (*): | 38890 |

Currently on list? (*): | short |

Submitted: | 3/6/2013 05:02:17 CDT |

Last modified: | 3/6/2013 05:50:25 CDT |

Database id: | 111497 |

Status Flags: | Verify |

Score (*): | 37.8517 (normalized score 0.001) |

#### 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.

- Generalized Lucas primitive part (archivable *)
- Prime on list:
yes, rank2

Subcategory: "Generalized Lucas primitive part"

(archival tag id 215199, tag last modified 2013-11-15 08:21:24)

#### 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 111497 person_id 9 machine Ditto P4 P4 what trial_divided notes Command: /home/ditto/client/pfgw -o -f -q"primV(27655,1,19926)" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] primV(27655,1,19926) 1/1 mro=0 trial factoring to 18883765 primV(27655,1,19926) has no small factor. [Elapsed time: 86.512 seconds] modified 2020-07-07 17:30:22 created 2013-03-06 05:05:02 id 153316

field value prime_id 111497 person_id 9 machine Ditto P4 P4 what prp notes Command: /home/ditto/client/pfgw -tc -q"primV(27655,1,19926)" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing primV(27655,1,19926) [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 23 Running N-1 test using base 53 Running N+1 test using discriminant 67, base 18+sqrt(67) Calling N-1 BLS with factored part 0.88% and helper 0.01% (2.64% proof) primV(27655,1,19926) is Fermat and Lucas PRP! (1723.2800s+0.1694s) [Elapsed time: 28.72 minutes] modified 2020-07-07 17:30:22 created 2013-03-06 05:08:02 id 153317

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

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