# (92365^{24691} - 1)/92364

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: | (92365^{24691} - 1)/92364 |
---|---|

Verification status (*): | PRP |

Official Comment (*): | Generalized repunit |

Unofficial Comments: | This prime has 2 user comments below. |

Proof-code(s): (*): | CH14 : Wu_T, CM, OpenPFGW, CHG |

Decimal Digits: | 122599 (log_{10} is 122598.37856424) |

Rank (*): | 45084 (digit rank is 1) |

Entrance Rank (*): | 44282 |

Currently on list? (*): | short |

Submitted: | 2/3/2024 22:22:10 UTC |

Last modified: | 2/4/2024 02:37:18 UTC |

Database id: | 137137 |

Status Flags: | Verify |

Score (*): | 40.1818 (normalized score 0.0082) |

#### Archival tags:

There are certain forms classed as archivable: these prime may (at times) remain on this list even if they do not make the Top 5000 proper. Such primes are tracked with archival tags.

- Generalized Repunit (archivable *)
- Prime on list:
yes, rank1

Subcategory: "Generalized Repunit"

(archival tag id 229268, tag last modified 2024-02-04 02:37:20)

#### 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 137137 person_id 9 machine Using: Digital Ocean Droplet what prp notes Command: /var/www/clientpool/1/pfgw64 -V -f -tc -q"(92365^24691-1)/92364" >command_output 2>&1

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

Primality testing (92365^24691-1)/92364 [N-1/N+1, Brillhart-Lehmer-Selfridge]

trial

Running N-1 test using base 3

Generic modular reduction using generic reduction FMA3 FFT length 40K, Pass1=640, Pass2=64, clm=2 on A 407263-bit number

Running N-1 test using base 7

Generic modular reduction using generic reduction FMA3 FFT length 40K, Pass1=640, Pass2=64, clm=2 on A 407263-bit number

Running N+1 test using discriminant 23, base 2+sqrt(23)

Generic modular reduction using generic reduction FMA3 FFT length 40K, Pass1=640, Pass2=64, clm=2 on A 407263-bit number

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

Iteration: 36/407284 ERROR: ROUND OFF 0.5>0.45

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

Running N+1 test using discriminant 23, base 2+sqrt(23)

Generic modular reduction using generic reduction FMA3 FFT length 48K, Pass1=768, Pass2=64, clm=2 on A 407263-bit number

Calling N-1 BLS with factored part 0.05% and helper 0.00% (0.15% proof)

(92365^24691-1)/92364 is Fermat and Lucas PRP! (1424.9318s+0.0013s)

[Elapsed time: 23.77 minutes]modified 2024-02-04 01:53:29 created 2024-02-04 01:29:43 id 182975

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

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