# 131814642^{65536} + 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: | 131814642^{65536} + 1 |
---|---|

Verification status (*): | Proven |

Official Comment (*): | Generalized Fermat |

Proof-code(s): (*): | L5101 : Candido, GFNSvCUDA, GeneFer, AthGFNSieve, PrimeGrid, LLR |

Decimal Digits: | 532150 (log_{10} is 532149.93805908) |

Rank (*): | 3374 (digit rank is 1) |

Entrance Rank (*): | 3255 |

Currently on list? (*): | yes |

Submitted: | 8/29/2021 07:20:18 CDT |

Last modified: | 8/29/2021 09:37:31 CDT |

Database id: | 132661 |

Status Flags: | TrialDiv |

Score (*): | 44.6965 (normalized score 1.2855) |

#### 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, rank595

Subcategory: "Generalized Fermat"

(archival tag id 226276, tag last modified 2021-10-22 22:37:19)

#### 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 132661 person_id 9 machine Using: Xeon (pool) 4c+4c 3.5GHz what prime notes Command: /home/caldwell/clientpool/1/pfgw64 -t -q"131814642^65536+1" 2>&1

PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8]

Primality testing 131814642^65536+1 [N-1, Brillhart-Lehmer-Selfridge]

F: 131814642^65536+1 108544/5594092 (trial factor to 202087058)

F: 131814642^65536+1 219136/5594092 (trial factor to 202087058)

F: 131814642^65536+1 329728/5594092 (trial factor to 202087058)

F: 131814642^65536+1 440320/5594092 (trial factor to 202087058)

F: 131814642^65536+1 550912/5594092 (trial factor to 202087058)

F: 131814642^65536+1 661504/5594092 (trial factor to 202087058)

Running N-1 test using base 5

Calling Brillhart-Lehmer-Selfridge with factored part 90.42%

131814642^65536+1 is prime! (7794.7953s+0.0060s)

[Elapsed time: 2.17 hours]modified 2021-08-29 09:30:56 created 2021-08-29 07:21:02 id 178373

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

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