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# (178^{87525} - 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: | (178^{87525} - 1)^{2} - 2 |
---|---|

Verification status (*): | Proven |

Official Comment (*): | [none] |

Unofficial Comments: | This prime has 2 user comments below. |

Proof-code(s): (*): | p392 : Batalov, Cksieve, OpenPFGW |

Decimal Digits: | 393937 (log_{10} is 393936.021404172) |

Rank (*): | 8043 (digit rank is 1) |

Entrance Rank (*): | 3654 |

Currently on list? (*): | no |

Submitted: | 5/21/2016 10:27:44 CDT |

Last modified: | 5/21/2016 17:35:08 CDT |

Removed (*): | 1/19/2018 16:15:38 CDT |

Database id: | 121680 |

Status Flags: | TrialDiv |

Score (*): | 43.7726 (normalized score 0.6335) |

#### User comments about this prime (disclaimer):

User comments are allowed to convey mathematical information about this number, how it was proven prime.... See our guidelines and restrictions.

#### 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 121680 person_id 9 machine Using: Xeon 4c+4c 3.5GHz what prime notes Command: /home/caldwell/client/pfgw/pfgw64 -tc -q"(178^87525-1)^2-2" 2>&1 PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing (178^87525-1)^2-2 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Running N-1 test using base 5 Running N+1 test using discriminant 13, base 2+sqrt(13) Running N+1 test using discriminant 13, base 3+sqrt(13) Calling N+1 BLS with factored part 50.00% and helper 0.00% (150.01% proof) (178^87525-1)^2-2 is prime! (24436.9732s+0.0114s) [Elapsed time: 6.79 hours] modified 2020-07-07 17:30:16 created 2016-05-21 10:31:02 id 167318

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

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