# (2^{688042} - 1)^{2} - 2

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: | (2^{688042} - 1)^{2} - 2 |
---|---|

Verification status (*): | Proven |

Official Comment (*): | [none] |

Proof-code(s): (*): | p393 : Rodenkirch, Cksieve, OpenPFGW |

Decimal Digits: | 414243 (log_{10} is 414242.560553274) |

Rank (*): | 7083 (digit rank is 1) |

Entrance Rank (*): | 2793 |

Currently on list? (*): | no |

Submitted: | 7/6/2016 17:18:01 CDT |

Last modified: | 7/7/2016 02:20:38 CDT |

Removed (*): | 1/31/2019 09:36:31 CDT |

Database id: | 121867 |

Status Flags: | TrialDiv |

Score (*): | 43.927 (normalized score 0.7312) |

#### 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 121867 person_id 9 machine Using: Xeon 4c+4c 3.5GHz what prime notes Command: /home/caldwell/client/pfgw/pfgw64 -tc -q"(2^688042-1)^2-2" 2>&1 PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing (2^688042-1)^2-2 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Running N+1 test using discriminant 17, base 1+sqrt(17) Running N+1 test using discriminant 17, base 2+sqrt(17) Calling N+1 BLS with factored part 50.01% and helper 0.00% (150.02% proof) (2^688042-1)^2-2 is prime! (31997.0740s+0.0078s) [Elapsed time: 8.89 hours] modified 2020-07-07 17:30:16 created 2016-07-06 17:21:01 id 167506

Query times: 0.0004 seconds to select prime, 0.0007 seconds to seek comments.

Printed from the PrimePages <primes.utm.edu> © Chris Caldwell.