# 2 · 7^{709976} + 2 · 7^{211441} + 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 · 7^{709976} + 2 · 7^{211441} + 1 |
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Verification status (*): | PRP |

Official Comment (*): | [none] |

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

Proof-code(s): (*): | CH9 : Zhou, OpenPFGW, CHG |

Decimal Digits: | 600000 (log_{10} is 599999.62708716) |

Rank (*): | 4380 (digit rank is 1) |

Entrance Rank (*): | 3801 |

Currently on list? (*): | yes |

Submitted: | 2/18/2023 19:28:03 UTC |

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

Database id: | 135387 |

Status Flags: | Verify |

Score (*): | 45.065 (normalized score 1.2793) |

#### 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 135387 person_id 9 machine Using: Dual Intel Xeon Gold 5222 CPUs 3.8GHz what prp notes Command: /home/caldwell/clientpool/1/pfgw64 -t -q"2*7^709976+2*7^211441+1" 2>&1

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

Primality testing 2*7^709976+2*7^211441+1 [N-1, Brillhart-Lehmer-Selfridge]

Running N-1 test using base 3

Calling Brillhart-Lehmer-Selfridge with factored part 29.78%

2*7^709976+2*7^211441+1 is PRP! (3891.1029s+0.0079s)

[Elapsed time: 64.85 minutes]modified 2023-02-18 20:37:08 created 2023-02-18 19:32:17 id 181167

Query times: 0.0005 seconds to select prime, 0.0004 seconds to seek comments.

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