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# (1549^{12973} - 1)/1548

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: | (1549^{12973} - 1)/1548 |
---|---|

Verification status (*): | PRP |

Official Comment (*): | Generalized repunit |

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

Proof-code(s): (*): | p170 : Wu_T, Primo, OpenPFGW |

Decimal Digits: | 41382 (log_{10} is 41381.347271634) |

Rank (*): | 57431 (digit rank is 1) |

Entrance Rank (*): | 31493 |

Currently on list? (*): | no |

Submitted: | 12/12/2010 12:55:04 CDT |

Last modified: | 12/12/2010 13:50:21 CDT |

Database id: | 96872 |

Status Flags: | Verify |

Score (*): | 36.8331 (normalized score 0.0006) |

#### 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 Repunit (archivable *)
- Prime on list:
no, rank22

Subcategory: "Generalized Repunit"

(archival tag id 213016, tag last modified 2020-08-21 16:20:26)

#### 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 96872 person_id 9 machine Ditto P4 P4 what trial_divided notes Command: /home/ditto/client/pfgw -o -f -q"(1549^12973-1)/1548" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] trial factoring to 13257035 (1549^12973-1)/1548 has no small factor. [Elapsed time: 44.319 seconds] modified 2020-07-07 17:30:32 created 2010-12-12 13:05:06 id 123133

field value prime_id 96872 person_id 9 machine Ditto P4 P4 what prp notes Command: /home/ditto/client/pfgw -tc -q"(1549^12973-1)/1548" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing (1549^12973-1)/1548 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(16384,20) to FFT(16384,19) Reduced from FFT(16384,19) to FFT(16384,18) Reduced from FFT(16384,18) to FFT(16384,17) 274940 bit request FFT size=(16384,17) Running N+1 test using discriminant 17, base 3+sqrt(17) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(16384,20) to FFT(16384,19) Reduced from FFT(16384,19) to FFT(16384,18) Reduced from FFT(16384,18) to FFT(16384,17) 274948 bit request FFT size=(16384,17) Calling N-1 BLS with factored part 0.25% and helper 0.02% (0.79% proof) (1549^12973-1)/1548 is Fermat and Lucas PRP! (764.8700s+0.0100s) [Elapsed time: 12.80 minutes] modified 2020-07-07 17:30:32 created 2010-12-12 13:09:19 id 123135

Query times: 0.0005 seconds to select prime, 0.0008 seconds to seek comments.

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