# (2^{5807} + 1)/3

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Description: | (2^{5807} + 1)/3 |
---|---|

Verification status (*): | PRP |

Official Comment (*): | Cyclotomy, generalized Lucas number, Wagstaff |

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

Proof-code(s): (*): | PM : Mihailescu |

Decimal Digits: | 1748 (log_{10} is 1747.60406357) |

Rank (*): | 103364 (digit rank is 4) |

Entrance Rank (*): | 19478 |

Currently on list? (*): | short |

Submitted: | 1998 |

Last modified: | 11/29/2004 15:55:01 CDT |

Database id: | 72546 |

Status Flags: | Verify |

Score (*): | 27.0163 (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.

- Cyclotomy Proof (tolerated *)
- Prime on list:
no, rank127

Subcategory: "Cyclotomy Proof"

(archival tag id 181341, tag last modified 2019-06-27 21:50:21)- Generalized Lucas Number (archivable *)
- Prime on list:
no, rank108

Subcategory: "Generalized Lucas Number"

(archival tag id 181340, tag last modified 2021-08-03 03:37:35)- Wagstaff (archivable *)
- Prime on list:
yes, rank9

Subcategory: "Wagstaff"

(archival tag id 181342, tag last modified 2021-08-03 03:37:36)

#### 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 72546 person_id 9 machine Linux P4 2.8GHz what prp notes Command: /home/caldwell/client/pfgw -f -tc -q"(2^5807+1)/3" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing (2^5807+1)/3 [N-1/N+1, Brillhart-Lehmer-Selfridge] trial factoring to 431245 Running N-1 test using base 2 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(768,22) to FFT(768,21) Reduced from FFT(768,21) to FFT(768,20) Reduced from FFT(768,20) to FFT(768,19) Reduced from FFT(768,19) to FFT(768,18) Reduced from FFT(768,18) to FFT(768,17) Reduced from FFT(768,17) to FFT(768,16) 11620 bit request FFT size=(768,16) Running N-1 test using base 5 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(768,22) to FFT(768,21) Reduced from FFT(768,21) to FFT(768,20) Reduced from FFT(768,20) to FFT(768,19) Reduced from FFT(768,19) to FFT(768,18) Reduced from FFT(768,18) to FFT(768,17) Reduced from FFT(768,17) to FFT(768,16) 11620 bit request FFT size=(768,16) Running N+1 test using discriminant 13, base 1+sqrt(13) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(768,22) to FFT(768,21) Reduced from FFT(768,21) to FFT(768,20) Reduced from FFT(768,20) to FFT(768,19) Reduced from FFT(768,19) to FFT(768,18) Reduced from FFT(768,18) to FFT(768,17) Reduced from FFT(768,17) to FFT(768,16) 11628 bit request FFT size=(768,16) Running N+1 test using discriminant 13, base 2+sqrt(13) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(768,22) to FFT(768,21) Reduced from FFT(768,21) to FFT(768,20) Reduced from FFT(768,20) to FFT(768,19) Reduced from FFT(768,19) to FFT(768,18) Reduced from FFT(768,18) to FFT(768,17) Reduced from FFT(768,17) to FFT(768,16) 11628 bit request FFT size=(768,16) Calling N+1 BLS with factored part 1.71% and helper 0.79% (5.94% proof) (2^5807+1)/3 is Fermat and Lucas PRP! (4.3552s+0.0003s) modified 2020-07-07 17:30:45 created 2004-11-29 15:55:56 id 77544

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

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