# 35 · 2^{831411} + 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: | 35 · 2^{831411} + 1 |
---|---|

Verification status (*): | Proven |

Official Comment (*): | Divides GF(831410,3) |

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

Proof-code(s): (*): | g279 : Cooper, NewPGen, PRP, Proth.exe |

Decimal Digits: | 250282 (log_{10} is 250281.19379303) |

Rank (*): | 22913 (digit rank is 1) |

Entrance Rank (*): | 160 |

Currently on list? (*): | no |

Submitted: | 6/5/2006 23:44:34 CDT |

Last modified: | 7/7/2006 00:52:55 CDT |

Database id: | 77910 |

Status Flags: | none |

Score (*): | 42.3781 (normalized score 0.1047) |

#### 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 Divisors (bases 3,5,6,10,12) (archivable *)
- Prime on list:
no, rank28, weight 45.933548120058

Subcategory: "Divides GF(*,3)"

(archival tag id 187116, tag last modified 2021-02-26 11:20:20)

#### 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 77910 person_id 9 machine WinXP Pent_M 1.7GHz Laptop what prime notes Command: pfgw.exe -n -t -q"35*2^831411+1" 2>&1 PFGW Version 20030811.Win_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Running N-1 test using base 3 N-1: 35*2^831411+1 622Primality testing 35*2^831411+1 [N-1, Brillhart-Lehmer-Selfridge] Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 35*2^831411+1 is prime! (9137.9324s+0.0457s) 500/831418 [Elapsed time: 9138 seconds] modified 2020-07-07 17:30:42 created 2006-06-06 00:44:43 id 84455

field value prime_id 77910 person_id 9 machine GenToo P3 400MHz what trial_divided notes Command: /home/caldwell/client/TrialDiv/TrialDiv -q 35 2 831411 1 2>&1 [Elapsed time: 9.839 seconds] modified 2020-07-07 17:30:42 created 2006-07-07 00:52:45 id 84638

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

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