# 147314 · 91^{392798} - 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: | 147314 · 91^{392798} - 1 |
---|---|

Verification status (*): | Proven |

Official Comment (*): | [none] |

Proof-code(s): (*): | A11 : Anonymous, Srsieve, CRUS, PRST |

Decimal Digits: | 769513 (log_{10} is 769512.70906496) |

Rank (*): | 3586 (digit rank is 1) |

Entrance Rank (*): | 3415 |

Currently on list? (*): | yes |

Submitted: | 1/24/2024 13:11:22 UTC |

Last modified: | 1/25/2024 03:37:25 UTC |

Database id: | 136931 |

Status Flags: | none |

Score (*): | 45.8289 (normalized score 2.4345) |

#### 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 136931 person_id 9 machine Using: Digital Ocean Droplet what prime notes Command: /var/www/clientpool/1/pfgw64 -V -f -tp -q"147314*91^392798-1" >command_output 2>&1

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

Primality testing 147314*91^392798-1 [N+1, Brillhart-Lehmer-Selfridge]

trial

Running N+1 test using discriminant 5, base 5+sqrt(5)

Special modular reduction using zero-padded AVX-512 FFT length 336K, Pass1=896, Pass2=384, clm=1 on 147314*91^392798-1

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

Iteration: 2902/2556267 ERROR: ROUND OFF 0.46727>0.45

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

Running N+1 test using discriminant 5, base 5+sqrt(5)

Special modular reduction using zero-padded AVX-512 FFT length 360K, Pass1=960, Pass2=384, clm=1 on 147314*91^392798-1

Calling Brillhart-Lehmer-Selfridge with factored part 56.86%

147314*91^392798-1 is prime! (23870.9925s+0.0098s)

[Elapsed time: 6.63 hours]modified 2024-01-25 03:20:12 created 2024-01-24 20:42:16 id 182769

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

Printed from the PrimePages <t5k.org> © Reginald McLean.