Migration complete - please let us know if anything isn't working.

# 287626 · 5^{277175} - 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: | 287626 · 5^{277175} - 1 |
---|---|

Verification status (*): | Proven |

Official Comment (*): | [none] |

Proof-code(s): (*): | p212 : Pinho, Srsieve, SierpinskiRiesel, PRP, OpenPFGW |

Decimal Digits: | 193743 (log_{10} is 193742.46977998) |

Rank (*): | 33144 (digit rank is 1) |

Entrance Rank (*): | 841 |

Currently on list? (*): | no |

Submitted: | 8/13/2008 06:00:38 UTC |

Last modified: | 3/11/2023 15:54:10 UTC |

Removed (*): | 2/26/2011 19:04:35 UTC |

Database id: | 85415 |

Status Flags: | none |

Score (*): | 41.5905 (normalized score 0.0416) |

#### 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 85415 person_id 9 machine Ditto P4 P4 what trial_divided notes Command: /home/ditto/client/TrialDiv/TrialDiv -q 287626 5 277175 -1 2>&1 [Elapsed time: 9.989 seconds] modified 2020-07-07 22:30:39 created 2008-08-13 06:05:01 id 100297

field value prime_id 85415 person_id 9 machine Ditto P4 P4 what prime notes Command: /home/ditto/client/pfgw -tp -q"287626*5^277175-1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 287626*5^277175-1 [N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 11, base 8+sqrt(11) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(81920,20) to FFT(81920,19) Reduced from FFT(81920,19) to FFT(81920,18) Reduced from FFT(81920,18) to FFT(81920,17) Reduced from FFT(81920,17) to FFT(81920,16) 1287214 bit request FFT size=(81920,16) Running N+1 test using discriminant 11, base 10+sqrt(11) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(81920,20) to FFT(81920,19) Reduced from FFT(81920,19) to FFT(81920,18) Reduced from FFT(81920,18) to FFT(81920,17) Reduced from FFT(81920,17) to FFT(81920,16) 1287214 bit request FFT size=(81920,16) Running N+1 test using discriminant 11, base 11+sqrt(11) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(81920,20) to FFT(81920,19) Reduced from FFT(81920,19) to FFT(81920,18) Reduced from FFT(81920,18) to FFT(81920,17) Reduced from FFT(81920,17) to FFT(81920,16) 1287214 bit request FFT size=(81920,16) Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 287626*5^277175-1 is prime! (-1824.3621s+0.0400s) [Elapsed time: 17.37 hours] modified 2020-07-07 22:30:39 created 2008-08-13 06:08:01 id 100298

Query times: 0.0003 seconds to select prime, 0.0006 seconds to seek comments.

Printed from the PrimePages <t5k.org> © Reginald McLean.