# 193786 · 5^{306459} - 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: | 193786 · 5^{306459} - 1 |
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Verification status (*): | Proven |

Official Comment (*): | [none] |

Proof-code(s): (*): | p215 : Lody, Srsieve, SierpinskiRiesel, PRP, OpenPFGW |

Decimal Digits: | 214211 (log_{10} is 214210.93588121) |

Rank (*): | 24904 (digit rank is 1) |

Entrance Rank (*): | 1328 |

Currently on list? (*): | no |

Submitted: | 5/27/2010 12:31:13 CDT |

Last modified: | 5/27/2010 19:50:23 CDT |

Removed (*): | 2/26/2012 12:06:22 CDT |

Database id: | 92876 |

Status Flags: | none |

Score (*): | 41.8995 (normalized score 0.0786) |

#### 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 92876 person_id 9 machine Ditto P4 P4 what trial_divided notes Command: /home/ditto/client/TrialDiv/TrialDiv -q 193786 5 306459 -1 2>&1 [Elapsed time: 9.614 seconds] modified 2020-07-07 17:30:34 created 2010-05-27 12:35:11 id 115135

field value prime_id 92876 person_id 9 machine Ditto P4 P4 what prime notes Command: /home/ditto/client/pfgw -tp -q"193786*5^306459-1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 193786*5^306459-1 [N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 13, base 6+sqrt(13) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(98304,20) to FFT(98304,19) Reduced from FFT(98304,19) to FFT(98304,18) Reduced from FFT(98304,18) to FFT(98304,17) Reduced from FFT(98304,17) to FFT(98304,16) 1423204 bit request FFT size=(98304,16) Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 193786*5^306459-1 is prime! (-660.1838s+0.0500s) [Elapsed time: 7.01 hours] modified 2020-07-07 17:30:34 created 2010-05-27 12:48:05 id 115137

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

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