# 31340 · 6^{833096} + 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: | 31340 · 6^{833096} + 1 |
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Verification status (*): | Proven |

Official Comment (*): | [none] |

Proof-code(s): (*): | p271 : Dettweiler, Srsieve, CRUS, OpenPFGW |

Decimal Digits: | 648280 (log_{10} is 648279.1901886) |

Rank (*): | 2408 (digit rank is 1) |

Entrance Rank (*): | 228 |

Currently on list? (*): | yes |

Submitted: | 9/27/2013 09:40:58 CDT |

Last modified: | 9/28/2013 15:50:26 CDT |

Database id: | 115647 |

Status Flags: | TrialDiv |

Score (*): | 45.3027 (normalized score 2.397) |

#### 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 115647 person_id 9 machine RedHat P4 P4 what prime notes Command: /home/caldwell/client/pfgw -t -q"31340*6^833096+1" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing 31340*6^833096+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 11 Running N-1 test using base 13 Running N-1 test using base 19 Running N-1 test using base 23 Running N-1 test using base 29 Calling Brillhart-Lehmer-Selfridge with factored part 61.31% 31340*6^833096+1 is prime! (106054.0387s+0.0296s) [Elapsed time: 29.46 hours] modified 2020-07-07 17:30:18 created 2013-09-27 09:53:01 id 161139

Query times: 0.0006 seconds to select prime, 0.0008 seconds to seek comments.

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