# (42^{159530} + 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.

#### This prime's information:

Description: | (42^{159530} + 1)^{2} - 2 |
---|---|

Verification status (*): | Proven |

Official Comment (*): | [none] |

Proof-code(s): (*): | p424 : Liiv, Cksieve, OpenPFGW |

Decimal Digits: | 517914 (log_{10} is 517913.91859435) |

Rank (*): | 5157 (digit rank is 1) |

Entrance Rank (*): | 4046 |

Currently on list? (*): | no |

Submitted: | 10/14/2021 11:31:01 CDT |

Last modified: | 10/15/2021 03:37:18 CDT |

Removed (*): | 7/30/2022 02:52:31 CDT |

Database id: | 132835 |

Status Flags: | TrialDiv |

Score (*): | 44.6132 (normalized score 0.9803) |

#### 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 132835 person_id 9 machine Using: Xeon (pool) 4c+4c 3.5GHz what prime notes Command: /home/caldwell/clientpool/1/pfgw64 -tc -q"(42^159530+1)^2-2" 2>&1 PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8] Primality testing (42^159530+1)^2-2 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 5 Running N+1 test using discriminant 13, base 1+sqrt(13) Running N+1 test using discriminant 13, base 2+sqrt(13) Calling N+1 BLS with factored part 50.00% and helper 0.00% (150.01% proof) (42^159530+1)^2-2 is prime! (57135.6132s+0.0050s) [Elapsed time: 15.87 hours] modified 2022-07-11 13:21:45 created 2021-10-14 11:36:02 id 178548

Query times: 0.0003 seconds to select prime, 0.0004 seconds to seek comments.

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