# 8435 · 2^{6786180} - 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.

Description: | 8435 · 2^{6786180} - 1 |
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Verification status (*): | Proven |

Official Comment (*): | [none] |

Proof-code(s): (*): | L4965 : Propper, LLR |

Decimal Digits: | 2042848 (log_{10} is 2042847.6620601) |

Rank (*): | 153 (digit rank is 1) |

Entrance Rank (*): | 108 |

Currently on list? (*): | short |

Submitted: | 1/7/2021 10:00:48 CDT |

Last modified: | 1/7/2021 15:50:21 CDT |

Database id: | 131549 |

Status Flags: | TrialDiv |

Score (*): | 48.8236 (normalized score 79.7119) |

#### 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 131549 person_id 9 machine Using: Xeon 4c+4c 3.5GHz what prime notes Command: /home/caldwell/client/llr.pl 8435*2^6786180-1 2>&1 Starting Lucas Lehmer Riesel prime test of 8435*2^6786180-1 Using AVX FFT length 560K, Pass1=448, Pass2=1280 V1 = 4 ; Computing U0... V1 = 4 ; Computing U0...done.Starting Lucas-Lehmer loop... 8435*2^6786180-1 is prime! (2042848 decimal digits) Time : 20157.383 sec. [Elapsed time: 5.60 hours] modified 2021-04-20 17:39:25 created 2021-01-07 10:01:01 id 177245

Query times: 0.0006 seconds to select prime, 0.0007 seconds to seek comments.

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