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# (2^{14479} + 1)/3

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: | (2^{14479} + 1)/3 |
---|---|

Verification status (*): | PRP |

Official Comment (*): | Generalized Lucas number, Wagstaff, ECPP |

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

Proof-code(s): (*): | c4 : Broadhurst, Primo |

Decimal Digits: | 4359 (log_{10} is 4358.13618596) |

Rank (*): | 86298 (digit rank is 1) |

Entrance Rank (*): | 35703 |

Currently on list? (*): | short |

Submitted: | 11/10/2004 02:21:59 CDT |

Last modified: | 6/3/2005 13:53:34 CDT |

Database id: | 74683 |

Status Flags: | Verify |

Score (*): | 29.8622 (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.

- Elliptic Curve Primality Proof (archivable *)
- Prime on list:
no, rank472

Subcategory: "ECPP"

(archival tag id 195466, tag last modified 2020-06-22 13:50:28)- Generalized Lucas Number (archivable *)
- Prime on list:
no, rank93

Subcategory: "Generalized Lucas Number"

(archival tag id 195465, tag last modified 2020-05-28 13:20:28)- Wagstaff (archivable *)
- Prime on list:
yes, rank3

Subcategory: "Wagstaff"

(archival tag id 195467, tag last modified 2014-09-17 12:50:33)

#### 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 74683 person_id 9 machine Linux P4 2.8GHz what prp notes Command: /home/caldwell/client/pfgw -f -tc -q"(2^14479+1)/3" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing (2^14479+1)/3 [N-1/N+1, Brillhart-Lehmer-Selfridge] trial factoring to 1168068 Running N-1 test using base 2 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(1792,21) to FFT(1792,20) Reduced from FFT(1792,20) to FFT(1792,19) Reduced from FFT(1792,19) to FFT(1792,18) Reduced from FFT(1792,18) to FFT(1792,17) 28964 bit request FFT size=(1792,17) Running N-1 test using base 3 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(1792,21) to FFT(1792,20) Reduced from FFT(1792,20) to FFT(1792,19) Reduced from FFT(1792,19) to FFT(1792,18) Reduced from FFT(1792,18) to FFT(1792,17) 28964 bit request FFT size=(1792,17) Running N+1 test using discriminant 7, base 1+sqrt(7) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(1792,21) to FFT(1792,20) Reduced from FFT(1792,20) to FFT(1792,19) Reduced from FFT(1792,19) to FFT(1792,18) Reduced from FFT(1792,18) to FFT(1792,17) 28972 bit request FFT size=(1792,17) Calling N-1 BLS with factored part 1.06% and helper 0.15% (3.34% proof) (2^14479+1)/3 is Fermat and Lucas PRP! (19.1013s+0.0003s) modified 2020-07-07 17:30:43 created 2005-06-03 16:53:22 id 79725

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

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