# 664342014133 · 2^{39840} + 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: | 664342014133 · 2^{39840} + 1 |
---|---|

Verification status (*): | Proven |

Official Comment (*): | Consecutive primes arithmetic progression (3,d=30) |

Proof-code(s): (*): | p408 : Batalov, PolySieve, OpenPFGW |

Decimal Digits: | 12005 (log_{10} is 12004.857418972) |

Rank (*): | 81483 (digit rank is 1) |

Entrance Rank (*): | 74336 |

Currently on list? (*): | short |

Submitted: | 4/27/2020 16:47:34 UTC |

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

Database id: | 130861 |

Status Flags: | none |

Score (*): | 33.0063 (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.

- Consecutive Primes in Arithmetic Progression (archivable class *)
- Prime on list:
yes, rank2

Subcategory: "Consecutive primes in arithmetic progression (3,d=*)"

(archival tag id 223982, tag last modified 2023-03-11 15:53:59)- Arithmetic Progressions of Primes (archivable class *)
- Prime on list:
no, rank132, weight 38.674096478692

Subcategory: "Arithmetic progression (3,d=*)"

(archival tag id 223983, tag last modified 2023-03-11 16:02:30)

#### 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 130861 person_id 9 machine Using: Xeon (pool) 4c+4c 3.5GHz what prime notes Command: /home/caldwell/clientpool/1/pfgw64 -t -q"664342014133*2^39840+1" 2>&1 PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8] Primality testing 664342014133*2^39840+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Calling Brillhart-Lehmer-Selfridge with factored part 99.90% 664342014133*2^39840+1 is prime! (1.1824s+0.0002s) [Elapsed time: 1.00 seconds] modified 2020-07-07 22:30:10 created 2020-04-27 16:51:11 id 176550

Query times: 0.0002 seconds to select prime, 0.0004 seconds to seek comments.

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