# (10^{657559} - 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: | (10^{657559} - 1)^{2} - 2 |
---|---|

Verification status (*): | Proven |

Official Comment (*): | Near-repdigit |

Proof-code(s): (*): | p405 : Propper, Cksieve, OpenPFGW |

Decimal Digits: | 1315118 (log_{10} is 1315118) |

Rank (*): | 640 (digit rank is 1) |

Entrance Rank (*): | 341 |

Currently on list? (*): | short |

Submitted: | 5/18/2022 12:17:57 UTC |

Last modified: | 5/20/2023 20:59:19 UTC |

Database id: | 133946 |

Status Flags: | none |

Score (*): | 47.4733 (normalized score 11.6403) |

#### Archival tags:

There are certain forms classed as archivable: these prime may (at times) remain on this list even if they do not make the Top 5000 proper. Such primes are tracked with archival tags.

- Near-repdigit (archivable *)
- Prime on list:
yes, rank12

Subcategory: "Near-repdigit"

(archival tag id 227062, tag last modified 2024-02-07 04:37:20)

#### 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 133946 person_id 9 machine Using: Dual Intel Xeon Gold 5222 CPUs 3.8GHz what prime notes Command: /home/caldwell/clientpool/1/pfgw64 -tc -q"(10^657559-1)^2-2" 2>&1 PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8] Primality testing (10^657559-1)^2-2 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Running N-1 test using base 7 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 50.00% and helper 0.00% (150.00% proof) (10^657559-1)^2-2 is prime! (218624.6174s+0.0102s) [Elapsed time: 2.53 days] modified 2022-07-11 18:21:44 created 2022-05-18 12:21:01 id 179670

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

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