# 174344 · 5^{855138} - 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: | 174344 · 5^{855138} - 1 |
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Verification status (*): | Proven |

Official Comment (*): | [none] |

Proof-code(s): (*): | L3354 : Willig, Srsieve, PrimeGrid, SierpinskiRiesel, LLR |

Decimal Digits: | 597722 (log_{10} is 597721.0529749) |

Rank (*): | 2782 (digit rank is 1) |

Entrance Rank (*): | 177 |

Currently on list? (*): | yes |

Submitted: | 1/9/2013 10:22:53 CDT |

Last modified: | 1/10/2013 08:20:26 CDT |

Database id: | 110673 |

Status Flags: | none |

Score (*): | 45.0533 (normalized score 1.8366) |

#### 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 110673 person_id 9 machine RedHat P4 P4 what prime notes Command: /home/caldwell/client/pfgw -tp -q"174344*5^855138-1" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing 174344*5^855138-1 [N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 3, base 1+sqrt(3) Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 174344*5^855138-1 is prime! (77903.3897s+0.0462s) [Elapsed time: 21.64 hours] modified 2020-07-07 17:30:23 created 2013-01-09 10:23:01 id 151620

field value prime_id 110673 person_id 9 machine Ditto P4 P4 what trial_divided notes Command: /home/ditto/client/TrialDiv/TrialDiv -q 174344 5 855138 -1 2>&1 [Elapsed time: 9.775 seconds] modified 2020-07-07 17:30:23 created 2013-01-09 10:35:02 id 151621

Query times: 0.0005 seconds to select prime, 0.0008 seconds to seek comments.

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