# Phi(6437, 10)

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: | Phi(6437, 10) |
---|---|

Verification status (*): | PRP |

Official Comment (*): | Unique, ECPP |

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

Proof-code(s): (*): | c47 : Chandler, Primo |

Decimal Digits: | 6240 (log_{10} is 6239.9542425094) |

Rank (*): | 83612 (digit rank is 1) |

Entrance Rank (*): | 44205 |

Currently on list? (*): | short |

Submitted: | 11/1/2008 08:21:36 CDT |

Last modified: | 11/3/2008 20:20:02 CDT |

Database id: | 85700 |

Status Flags: | Verify |

Score (*): | 30.9772 (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.

- Unique (archivable *)
- Prime on list:
yes, rank20

Subcategory: "Unique"

(archival tag id 210376, tag last modified 2021-06-05 00:37:32)- Elliptic Curve Primality Proof (archivable *)
- Prime on list:
no, rank367

Subcategory: "ECPP"

(archival tag id 210375, tag last modified 2021-09-18 09:37:41)

#### 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 85700 person_id 9 machine RedHat P4 P4 what trial_divided notes Command: /home/caldwell/client/pfgw -o -f -q"Phi(6437,10)" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] trial factoring to 1724500 Phi(6437,10) has no small factor. [Elapsed time: 1.021 seconds] modified 2020-07-07 17:30:39 created 2008-11-01 08:22:01 id 100871

field value prime_id 85700 person_id 9 machine RedHat P4 P4 what prp notes Command: /home/caldwell/client/pfgw -t -q"Phi(6437,10)" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing Phi(6437,10) [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(2560,21) to FFT(2560,20) Reduced from FFT(2560,20) to FFT(2560,19) Reduced from FFT(2560,19) to FFT(2560,18) Reduced from FFT(2560,18) to FFT(2560,17) 41466 bit request FFT size=(2560,17) Running N-1 test using base 7 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(2560,21) to FFT(2560,20) Reduced from FFT(2560,20) to FFT(2560,19) Reduced from FFT(2560,19) to FFT(2560,18) Reduced from FFT(2560,18) to FFT(2560,17) 41466 bit request FFT size=(2560,17) Running N-1 test using base 11 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(2560,21) to FFT(2560,20) Reduced from FFT(2560,20) to FFT(2560,19) Reduced from FFT(2560,19) to FFT(2560,18) Reduced from FFT(2560,18) to FFT(2560,17) 41466 bit request FFT size=(2560,17) Running N-1 test using base 17 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(2560,21) to FFT(2560,20) Reduced from FFT(2560,20) to FFT(2560,19) Reduced from FFT(2560,19) to FFT(2560,18) Reduced from FFT(2560,18) to FFT(2560,17) 41466 bit request FFT size=(2560,17) Calling Brillhart-Lehmer-Selfridge with factored part 1.27% Phi(6437,10) is PRP! (17.3800s+0.0000s) [Elapsed time: 17.00 seconds] modified 2020-07-07 17:30:39 created 2008-11-01 08:23:02 id 100872

Query times: 0.0003 seconds to select prime, 0.0007 seconds to seek comments.

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