# 1361244^{131072} + 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: | 1361244^{131072} + 1 |
---|---|

Verification status (*): | Proven |

Official Comment (*): | Generalized Fermat |

Proof-code(s): (*): | g236 : Heuer, GFN17Sieve, GFNSearch, Proth.exe |

Decimal Digits: | 803988 (log_{10} is 803987.25657578) |

Rank (*): | 3602 (digit rank is 1) |

Entrance Rank (*): | 9 |

Currently on list? (*): | short |

Submitted: | 7/9/2004 09:17:05 UTC |

Last modified: | 3/11/2023 15:54:10 UTC |

Database id: | 70924 |

Status Flags: | none |

Score (*): | 45.9635 (normalized score 2.5393) |

#### 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, rank1318

Subcategory: "Generalized Fermat"

(archival tag id 204696, tag last modified 2024-07-19 03:37:18)

#### 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 70924 person_id 9 machine Linux P4 2.8GHz what prime notes Command: /home/caldwell/client/pfgw -f -t -q"1361244^131072+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 1361244^131072+1 [N-1, Brillhart-Lehmer-Selfridge] trial factoring to 313033767 Running N-1 test using base 5 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(393216,19) to FFT(393216,18) Reduced from FFT(393216,18) to FFT(393216,17) Reduced from FFT(393216,17) to FFT(393216,16) 5341584 bit request FFT size=(393216,16) Calling Brillhart-Lehmer-Selfridge with factored part 82.41% 1361244^131072+1 is prime! (289063.3696s+0.3350s) modified 2020-07-07 22:30:45 created 2004-07-09 09:23:00 id 75899

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

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