# 3^{2095902} + 3^{647322} - 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: | 3^{2095902} + 3^{647322} - 1 |
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Verification status (*): | PRP |

Official Comment (*): | [none] |

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

Proof-code(s): (*): | x44 : Zhou, Unknown |

Decimal Digits: | 1000000 (log_{10} is 999999.39200945) |

Rank (*): | 1646 (digit rank is 2) |

Entrance Rank (*): | 380 |

Currently on list? (*): | short |

Submitted: | 8/8/2018 09:57:27 CDT |

Last modified: | 8/9/2018 17:20:20 CDT |

Database id: | 125529 |

Status Flags: | Verify, TrialDiv |

Score (*): | 46.633 (normalized score 7.216) |

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

User comments are allowed to convey mathematical information about this number, how it was proven prime.... See our guidelines and restrictions.

#### 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 125529 person_id 9 machine Using: Xeon (pool) 4c+4c 3.5GHz what prp notes Command: /home/caldwell/clientpool/1/pfgw64 -tp -q"3^2095902+3^647322-1" 2>&1 PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing 3^2095902+3^647322-1 [N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 3, base 3+sqrt(3) Calling Brillhart-Lehmer-Selfridge with factored part 30.89% 3^2095902+3^647322-1 is Lucas PRP! (110619.4077s+0.0441s) [Elapsed time: 30.73 hours] modified 2020-07-07 17:30:14 created 2018-08-08 10:13:02 id 171203

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

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