# 334310 · 211^{334310} - 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: | 334310 · 211^{334310} - 1 |
---|---|

Verification status (*): | Proven |

Official Comment (*): | Generalized Woodall |

Proof-code(s): (*): | p350 : Koen, Gcwsieve, GenWoodall, OpenPFGW |

Decimal Digits: | 777037 (log_{10} is 777036.39177994) |

Rank (*): | 1869 (digit rank is 1) |

Entrance Rank (*): | 78 |

Currently on list? (*): | short |

Submitted: | 4/11/2012 23:40:42 CDT |

Last modified: | 4/14/2012 02:20:22 CDT |

Database id: | 106236 |

Status Flags: | none |

Score (*): | 45.8588 (normalized score 4.1139) |

#### 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 Woodall (archivable *)
- Prime on list:
yes, rank7

Subcategory: "Generalized Woodall"

(archival tag id 214301, tag last modified 2019-11-26 12:20:12)

#### 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 106236 person_id 9 machine RedHat P4 P4 what trial_divided notes Command: /home/caldwell/client/TrialDiv/TrialDiv -q 334310 211 334310 -1 2>&1 [Elapsed time: 9.873 seconds] modified 2020-07-07 17:30:26 created 2012-04-11 23:48:01 id 142062

field value prime_id 106236 person_id 9 machine RedHat P4 P4 what prime notes Command: /home/caldwell/client/pfgw -tp -q"334310*211^334310-1" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing 334310*211^334310-1 [N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 7, base 1+sqrt(7) Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 334310*211^334310-1 is prime! (180542.2381s+0.0672s) [Elapsed time: 2.09 days] modified 2020-07-07 17:30:26 created 2012-04-11 23:53:01 id 142063

Query times: 0.0004 seconds to select prime, 0.0006 seconds to seek comments.

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