# 45 · 2^{368553} - 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: | 45 · 2^{368553} - 1 |
---|---|

Verification status (*): | Proven |

Official Comment (*): | Arithmetic progression (2,d=45*2^368553-405769059*2^180009) [p108] |

Proof-code(s): (*): | L4 : Sun, NewPGen, LLR |

Decimal Digits: | 110948 (log_{10} is 110947.16120446) |

Rank (*): | 43045 (digit rank is 2) |

Entrance Rank (*): | 176 |

Currently on list? (*): | no |

Submitted: | 3/7/2003 01:46:40 CDT |

Last modified: | 3/7/2003 01:46:40 CDT |

Database id: | 64104 |

Status Flags: | none |

Score (*): | 39.8743 (normalized score 0.0085) |

#### 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.

- Arithmetic Progressions of Primes (archivable class *)
- Prime on list:
no, rank22

Subcategory: "Arithmetic progression (2,d=*)"

(archival tag id 187580, tag last modified 2020-04-08 13:50:11)

#### 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 64104 person_id 9 machine Linux P4 2.8GHz what prime notes PFGW Version 20020311.x86_Dev (Alpha software, 'caveat utilitor') Running N+1 test using discriminant 7, base 1+sqrt(7) Primality testing 45*2^368553-1 [N+1, Brillhart-Lehmer-Selfridge] Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 45*2^368553-1 is prime! (882.242704 seconds) modified 2003-03-25 11:21:39 created 2003-03-07 11:33:06 id 68591

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

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