# Phi(5, (3668 · 16001# - 1) · (378266 · 16001#/5 + 1)^{7})

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: | Phi(5, (3668 · 16001# - 1) · (378266 · 16001#/5 + 1)^{7}) |
---|---|

Verification status (*): | PRP |

Official Comment (*): | Generalized unique |

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

Proof-code(s): (*): | x34 : Broadhurst, Caldwell, OpenPFGW |

Decimal Digits: | 221071 (log_{10} is 221070.87932347) |

Rank (*): | 27542 (digit rank is 1) |

Entrance Rank (*): | 505 |

Currently on list? (*): | no |

Submitted: | 10/1/2008 14:45:28 UTC |

Last modified: | 3/11/2023 15:54:10 UTC |

Database id: | 85584 |

Status Flags: | Verify |

Score (*): | 41.9964 (normalized score 0.0601) |

#### 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 Unique (archivable *)
- Prime on list:
no, rank157

Subcategory: "Generalized Unique"

(archival tag id 224226, tag last modified 2023-09-12 04:37:20)

#### 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 85584 person_id 9 machine RedHat P4 P4 what trial_divided notes Command: /home/caldwell/client/pfgw -o -f -q"Phi(5,(3668*16001#-1)*(378266*16001#/5+1)^7)" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] trial factoring to 79437167 Phi(5,(3668*16001#-1)*(378266*16001#/5+1)^7) has no small factor. [Elapsed time: 1289.182 seconds] modified 2020-07-07 22:30:39 created 2008-10-01 14:52:01 id 100637

field value prime_id 85584 person_id 9 machine RedHat P4 P4 what prp notes Command: /home/caldwell/client/pfgw -tc -hhelper -q"Phi(5,(3668*16001#-1)*(378266*16001#/5+1)^7)" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing Phi(5,(3668*16001#-1)*(378266*16001#/5+1)^7) [N-1/N+1, Brillhart-Lehmer-Selfridge] Reading factors from helper file helper Running N-1 test using base 16033 Running N-1 test using base 16061 Running N-1 test using base 16063 Running N-1 test using base 16067 Running N+1 test using discriminant 16103, base 6+sqrt(16103) Calling N-1 BLS with factored part 28.13% and helper 0.00% (84.38% proof) Phi(5,(3668*16001#-1)*(378266*16001#/5+1)^7) is Fermat and Lucas PRP! (95089.6385s+0.4037s) [Elapsed time: 26.41 hours] modified 2020-07-07 22:30:39 created 2008-10-03 17:01:40 id 100652

Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.

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