# 729 · 2^{716258} + 1

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: | 729 · 2^{716258} + 1 |
---|---|

Verification status (*): | Proven |

Official Comment (*): | Generalized Fermat |

Proof-code(s): (*): | L1238 : Dovgiy, Srsieve, PrimeGrid, LLR |

Decimal Digits: | 215619 (log_{10} is 215618.00536182) |

Rank (*): | 24645 (digit rank is 1) |

Entrance Rank (*): | 991 |

Currently on list? (*): | no |

Submitted: | 2/15/2010 09:41:41 CDT |

Last modified: | 2/15/2010 13:50:22 CDT |

Removed (*): | 3/4/2012 00:13:53 CDT |

Database id: | 91775 |

Status Flags: | none |

Score (*): | 41.9196 (normalized score 0.0814) |

#### 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 Fermat (archivable *)
- Prime on list:
no, rank2026

Subcategory: "Generalized Fermat"

(archival tag id 210610, tag last modified 2021-09-15 20:37:17)

#### 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 91775 person_id 9 machine RedHat P4 P4 what trial_divided notes Command: /home/caldwell/client/TrialDiv/TrialDiv -q 729 2 716258 1 2>&1 [Elapsed time: 10.298 seconds] modified 2020-07-07 17:30:36 created 2010-02-15 09:48:02 id 112923

field value prime_id 91775 person_id 9 machine Ditto P4 P4 what prime notes Command: /home/ditto/client/pfgw -t -q"729*2^716258+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 729*2^716258+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 5 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(98304,20) to FFT(98304,19) Reduced from FFT(98304,19) to FFT(98304,18) Reduced from FFT(98304,18) to FFT(98304,17) Reduced from FFT(98304,17) to FFT(98304,16) 1432544 bit request FFT size=(98304,16) Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 729*2^716258+1 is prime! (-1101.5873s+0.0000s) [Elapsed time: 53.87 minutes] modified 2020-07-07 17:30:36 created 2010-02-15 12:35:08 id 112934

Query times: 0.0002 seconds to select prime, 0.0004 seconds to seek comments.

Printed from the PrimePages <primes.utm.edu> © Chris Caldwell.