# 1 - V( - 2, - 2, 3074821) - 2^{3074821}

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#### This prime's information:

Description: | 1 - V( - 2, - 2, 3074821) - 2^{3074821} |
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Verification status (*): | Proven |

Official Comment (*): | [none] |

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

Proof-code(s): (*): | p437 : Propper, Batalov, EMsieve, PIES, OpenPFGW |

Decimal Digits: | 1342125 (log_{10} is 1342124.8411758) |

Rank (*): | 693 (digit rank is 1) |

Entrance Rank (*): | 684 |

Currently on list? (*): | yes |

Submitted: | 10/30/2024 18:23:07 UTC |

Last modified: | 11/1/2024 16:37:15 UTC |

Database id: | 138687 |

Status Flags: | none |

Score (*): | 47.5356 (normalized score 11.1608) |

#### 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 138687 person_id 9 machine Using: Digital Ocean Droplet what prime notes Command: /var/www/clientpool/1/pfgw64 -V -f -tc -q"1-lucasV(-2,-2,3074821)-2^3074821" >command_output 2>&1

PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]

Primality testing 1-lucasV(-2,-2,3074821)-2^3074821 [N-1/N+1, Brillhart-Lehmer-Selfridge]

trial

Running N-1 test using base 5

Generic modular reduction using generic reduction AVX-512 FFT length 448K, Pass1=1K, Pass2=448, clm=1 on A 4458444-bit number

Detected in MAXERR>0.45 (round off check) in Exponentiator::Iterate

Iteration: 38399/4458777 ERROR: ROUND OFF 0.47328>0.45

(Test aborted, try again using the -a1 switch)

Running N-1 test using base 29

Generic modular reduction using generic reduction AVX-512 FFT length 480K, Pass1=960, Pass2=512, clm=1 on A 4458444-bit number

Running N+1 test using discriminant 41, base 1+sqrt(41)

Generic modular reduction using generic reduction AVX-512 FFT length 448K, Pass1=1K, Pass2=448, clm=1 on A 4458444-bit number

Detected in MAXERR>0.45 (round off check) in Exponentiator::Iterate

Iteration: 40/4458444 ERROR: ROUND OFF 0.49387>0.45

(Test aborted, try again using the -a1 switch)

Running N+1 test using discriminant 41, base 1+sqrt(41)

Generic modular reduction using generic reduction AVX-512 FFT length 480K, Pass1=960, Pass2=512, clm=1 on A 4458444-bit number

Calling N-1 BLS with factored part 34.49% and helper 0.00% (103.46% proof)

1-lucasV(-2,-2,3074821)-2^3074821 is prime! (164221.5108s+0.0646s)

[Elapsed time: 1.90 days]modified 2024-11-01 16:01:03 created 2024-10-30 18:24:01 id 184530

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

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