# 205833 · 2^{2976222} - 411665

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: | 205833 · 2^{2976222} - 411665 |
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Verification status (*): | Proven |

Official Comment (*): | [none] |

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

Proof-code(s): (*): | L4667 : Morelli, LLR |

Decimal Digits: | 895938 (log_{10} is 895937.40927005) |

Rank (*): | 3184 (digit rank is 1) |

Entrance Rank (*): | 349 |

Currently on list? (*): | short |

Submitted: | 8/20/2017 10:23:00 UTC |

Last modified: | 3/11/2023 15:54:10 UTC |

Database id: | 123859 |

Status Flags: | none |

Score (*): | 46.2958 (normalized score 3.6294) |

#### 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 123859 person_id 9 machine Using: Xeon (pool) 4c+4c 3.5GHz what prime notes Command: /home/caldwell/clientpool/1/pfgw64 -t -hhelper -q"205833*2^2976222-411665" 2>&1 PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing 205833*2^2976222-411665 [N-1, Brillhart-Lehmer-Selfridge] Reading factors from helper file helper Running N-1 test using base 3 Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 205833*2^2976222-411665 is prime! (35295.7567s+0.0011s) [Elapsed time: 9.80 hours] Helper File: 2^2976221-1 modified 2020-07-07 22:30:15 created 2017-08-26 17:13:44 id 169527

Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.

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