# 612563306175 · 2^{1290000} - 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: | 612563306175 · 2^{1290000} - 1 |
---|---|

Verification status (*): | Proven |

Official Comment (*): | Arithmetic progression (1,d=175578398085*2^1290001) [p199] |

Proof-code(s): (*): | L2345 : Boerner, TwinGen, PrimeGrid, LLR |

Decimal Digits: | 388341 (log_{10} is 388340.48155751) |

Rank (*): | 13997 (digit rank is 1183) |

Entrance Rank (*): | 1241 |

Currently on list? (*): | no |

Submitted: | 5/21/2013 19:08:29 CDT |

Last modified: | 10/1/2015 20:25:34 CDT |

Database id: | 114202 |

Status Flags: | none |

Score (*): | 43.7286 (normalized score 0.3963) |

#### 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, rank10

Subcategory: "Arithmetic progression (1,d=*)"

(archival tag id 218095, tag last modified 2021-09-24 02:37:50)

#### 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 114202 person_id 9 machine RedHat P4 P4 what trial_divided notes Command: /home/caldwell/client/TrialDiv/TrialDiv -q 612563306175 2 1290000 -1 2>&1 [Elapsed time: 10.320 seconds] modified 2020-07-07 17:30:19 created 2013-05-21 19:18:01 id 158781

field value prime_id 114202 person_id 9 machine RedHat P4 P4 what prime notes Command: /home/caldwell/client/llr.pl 612563306175*2^1290000-1 2>&1 Starting Lucas Lehmer Riesel prime test of 612563306175*2^1290000-1 Using Zero Padded IBDWT : Mersenne fftlen = 65536, Used fftlen = 131072 V1 = 5 ; Computing U0... V1 = 5 ; Computing U0...done. Starting Lucas-Lehmer loop... 612563306175*2^1290000-1 is prime! Time : 5361.708 sec. [Elapsed time: 89.37 minutes] modified 2020-07-07 17:30:19 created 2013-05-21 19:23:01 id 158782

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

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