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# 2109 · 2^{3423798} - 3027 · 2^{988658} + 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: | 2109 · 2^{3423798} - 3027 · 2^{988658} + 1 |
---|---|

Verification status (*): | PRP |

Official Comment (*): | Arithmetic progression (3,d=2109*2^3423797-3027*2^988658) |

Unofficial Comments: | This prime has 1 user comment below. |

Proof-code(s): (*): | CH13 : Propper, Batalov, EMsieve, OpenPFGW, CHG |

Decimal Digits: | 1030670 (log_{10} is 1030669.2211709) |

Rank (*): | 1338 (digit rank is 1) |

Entrance Rank (*): | 1030 |

Currently on list? (*): | short |

Submitted: | 1/2/2023 00:31:17 UTC |

Last modified: | 3/11/2023 16:02:24 UTC |

Database id: | 134725 |

Status Flags: | Verify, TrialDiv |

Score (*): | 46.7257 (normalized score 7.0771) |

#### 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:
yes, rank2, weight 54.619807455939

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

(archival tag id 227601, tag last modified 2023-03-11 16:02:32)

#### User comments about this prime (disclaimer):

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#### 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 134725 person_id 9 machine Using: Dual Intel Xeon Gold 5222 CPUs 3.8GHz what prp notes Command: /home/caldwell/clientpool/1/pfgw64 -t -q"2109*2^3423798-3027*2^988658+1" 2>&1

PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8]

Primality testing 2109*2^3423798-3027*2^988658+1 [N-1, Brillhart-Lehmer-Selfridge]

Running N-1 test using base 7

Calling Brillhart-Lehmer-Selfridge with factored part 28.88%

2109*2^3423798-3027*2^988658+1 is PRP! (12120.1890s+0.0007s)

[Elapsed time: 3.37 hours]modified 2023-01-02 03:55:02 created 2023-01-02 00:33:01 id 180505

Query times: 0.0005 seconds to select prime, 0.0005 seconds to seek comments.

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