# 3 · 2^{5082306} + 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: | 3 · 2^{5082306} + 1 |
---|---|

Verification status (*): | Proven |

Official Comment (*): | Divides GF(5082303,3), GF(5082305,5) |

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

Proof-code(s): (*): | L780 : Brady, Srsieve, PrimeGrid, LLR |

Decimal Digits: | 1529928 (log_{10} is 1529927.0302643) |

Rank (*): | 344 (digit rank is 1) |

Entrance Rank (*): | 15 |

Currently on list? (*): | short |

Submitted: | 4/4/2009 09:54:03 CDT |

Last modified: | 4/16/2009 13:50:03 CDT |

Database id: | 87449 |

Status Flags: | none |

Score (*): | 47.9373 (normalized score 25.9079) |

#### 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:
yes, rank7, weight 49.035923447264

Subcategory: "Divides GF(*,3)"

(archival tag id 208974, tag last modified 2020-10-29 19:20:16)- Generalized Fermat Divisors (bases 3,5,6,10,12) (archivable *)
- Prime on list:
yes, rank6, weight 49.035923447264

Subcategory: "Divides GF(*,5)"

(archival tag id 208975, tag last modified 2020-10-29 19:20:16)

#### 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 87449 person_id 9 machine RedHat P4 P4 what trial_divided notes Command: /home/caldwell/client/TrialDiv/TrialDiv -q 3 2 5082306 1 2>&1 [Elapsed time: 10.697 seconds] modified 2020-07-07 17:30:38 created 2009-04-04 09:59:11 id 104262

field value prime_id 87449 person_id 9 machine RedHat P4 P4 what prime notes Command: /home/caldwell/client/pfgw -t -q"3*2^5082306+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 3*2^5082306+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(786432,19) to FFT(786432,18) Reduced from FFT(786432,18) to FFT(786432,17) Reduced from FFT(786432,17) to FFT(786432,16) 10164624 bit request FFT size=(786432,16) Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 3*2^5082306+1 is prime! (-1634.5699s+0.0100s) [Elapsed time: 3.72 days] modified 2020-07-07 17:30:38 created 2009-04-04 10:23:02 id 104263

Query times: 0.0003 seconds to select prime, 0.0005 seconds to seek comments.

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