# (2^{28771} - 1)/104726441

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Description: | (2^{28771} - 1)/104726441 |
---|---|

Verification status (*): | PRP |

Official Comment (*): | Mersenne cofactor, ECPP |

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

Proof-code(s): (*): | c56 : Soule, Minovic, OpenPFGW, Primo |

Decimal Digits: | 8653 (log_{10} is 8652.9139489036) |

Rank (*): | 79023 (digit rank is 1) |

Entrance Rank (*): | 58036 |

Currently on list? (*): | short |

Submitted: | 2/6/2012 22:58:18 CDT |

Last modified: | 2/6/2012 23:20:27 CDT |

Database id: | 104244 |

Status Flags: | Verify |

Score (*): | 31.9915 (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, rank256

Subcategory: "ECPP"

(archival tag id 213861, tag last modified 2021-09-18 09:37:41)- Mersenne cofactor (archivable *)
- Prime on list:
yes, rank15

Subcategory: "Mersenne cofactor"

(archival tag id 213862, tag last modified 2021-02-24 00:50:28)

#### 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 104244 person_id 9 machine Ditto P4 P4 what trial_divided notes Command: /home/ditto/client/pfgw -o -f -q"(2^28771-1)/104726441" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] (2^28771-1)/104726441 1/1 mro=0 trial factoring to 2457184 (2^28771-1)/104726441 has no small factor. [Elapsed time: 1.951 seconds] modified 2020-07-07 17:30:29 created 2012-02-06 23:05:02 id 138078

field value prime_id 104244 person_id 9 machine Ditto P4 P4 what prp notes Command: /home/ditto/client/pfgw -tc -q"(2^28771-1)/104726441" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing (2^28771-1)/104726441 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 5 Running N+1 test using discriminant 17, base 1+sqrt(17) Calling N+1 BLS with factored part 0.18% and helper 0.13% (0.68% proof) (2^28771-1)/104726441 is Fermat and Lucas PRP! (29.6894s+0.0003s) [Elapsed time: 30.00 seconds] modified 2020-07-07 17:30:29 created 2012-02-06 23:08:01 id 138079

Query times: 0.0004 seconds to select prime, 0.0007 seconds to seek comments.

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