# 2 · 10^{19233} - 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: | 2 · 10^{19233} - 1 |
---|---|

Verification status (*): | Proven |

Official Comment (*): | Near-repdigit |

Proof-code(s): (*): | g200 : Clarkson, Proth.exe |

Decimal Digits: | 19234 (log_{10} is 19233.301029996) |

Rank (*): | 74680 (digit rank is 1) |

Entrance Rank (*): | 2831 |

Currently on list? (*): | no |

Submitted: | 9/21/2000 22:22:27 UTC |

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

Database id: | 9814 |

Status Flags: | none |

Score (*): | 34.4653 (normalized score 0) |

#### 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:
no, rank192

Subcategory: "Near-repdigit"

(archival tag id 211141, 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 9814 person_id 9 machine Windows XP P4 1.8GHz what prime notes Primality testing 2*10^19233-1 [N+1, Brillhart-Lehmer-Selfridge] Calling Brillhart-Lehmer-Selfridge with factored part 69.90% 2*10^19233-1 is prime! (950.529000 seconds) PFGW Version 1.1 for Windows Running N+1 test using discriminant 3, base 1+sqrt(3) Running N+1 test using discriminant 3, base 3+sqrt(3) Running N+1 test using discriminant 3, base 6+sqrt(3) modified 2003-03-25 17:25:02 created 2002-12-12 22:48:31 id 39160

Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.

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