# 11754128376394782080351\

49360635999371658705159870633484377238553812244526\

11844232886228245901292532817349347812678729023786^{8192} + 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.

#### This prime's information:

Description: | 11754128376394782080351\ 49360635999371658705159870633484377238553812244526\ 11844232886228245901292532817349347812678729023786 ^{8192} + 1 |
---|---|

Verification status (*): | Proven |

Official Comment (*): | Generalized Fermat |

Unofficial Comments: | This prime has 2 user comments below. |

Proof-code(s): (*): | p416 : Monnin, LLR2, PrivGfnServer, OpenPFGW |

Decimal Digits: | 1000000 (log_{10} is 999999) |

Rank (*): | 2583 (digit rank is 17) |

Entrance Rank (*): | 985 |

Currently on list? (*): | short |

Submitted: | 4/6/2021 18:32:23 UTC |

Last modified: | 6/10/2023 03:37:14 UTC |

Database id: | 132212 |

Status Flags: | none |

Score (*): | 46.633 (normalized score 5.426) |

#### 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, rank987

Subcategory: "Generalized Fermat"

(archival tag id 226081, tag last modified 2024-03-01 23:37:20)

#### 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 132212 person_id 9 machine Using: Digital Ocean Droplet what prime notes PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]

Primality testing 1175412837...8729023786^8192+1 [N-1, Brillhart-Lehmer-Selfridge]

Reading factors from helper file p_132212

trial

Running N-1 test using base 3

Generic modular reduction using generic reduction FMA3 FFT length 336K, Pass1=448, Pass2=768, clm=4 on A 3321925-bit number

Calling Brillhart-Lehmer-Selfridge with factored part 41.51%

1175412837...8729023786^8192+1 is prime! (57524.7720s+0.0104s)

[Elapsed time: 15.98 hours]

Helper File:

102934239816486361102607080101997899898038675281

473777469634854139236065334735086157108209901510149modified 2023-06-10 03:37:14 created 2023-06-09 11:38:29 id 181981

field value prime_id 132212 person_id 9 machine Using: Xeon (pool) 4c+4c 3.5GHz what prp notes PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8] Primality testing 1175412837...8729023786^8192+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Running N-1 test using base 5 Calling Brillhart-Lehmer-Selfridge with factored part 5.53% 1175412837...8729023786^8192+1 is PRP! (45003.2256s+0.1739s) [Elapsed time: 12.50 hours] modified 2021-04-20 22:39:24 created 2021-04-06 18:36:01 id 177911

Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.

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