# primA(413205)

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: | primA(413205) |
---|---|

Verification status (*): | PRP |

Official Comment (*): | Lucas Aurifeuillian primitive part, ECPP |

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

Proof-code(s): (*): | E1 : Batalov, CM |

Decimal Digits: | 21127 (log_{10} is 21126.140712854) |

Rank (*): | 71461 (digit rank is 1) |

Entrance Rank (*): | 71405 |

Currently on list? (*): | short |

Submitted: | 9/17/2023 08:59:20 UTC |

Last modified: | 9/17/2023 09:37:11 UTC |

Database id: | 136449 |

Status Flags: | Verify |

Score (*): | 34.7557 (normalized score 0) |

#### 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.

- Lucas Aurifeuillian primitive part (archivable *)
- Prime on list:
yes, rank3

Subcategory: "Lucas Aurifeuillian primitive part"

(archival tag id 228822, tag last modified 2023-10-03 00:37:15)- Elliptic Curve Primality Proof (archivable *)
- Prime on list:
no, rank71

Subcategory: "ECPP"

(archival tag id 228823, tag last modified 2023-10-03 00:37:15)

#### 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 136449 person_id 9 machine Using: Digital Ocean Droplet what prp notes PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]

Primality testing 1382651896...2487135601 [N-1/N+1, Brillhart-Lehmer-Selfridge]

trial

Running N-1 test using base 7

Generic modular reduction using generic reduction AVX-512 FFT length 7K on A 70180-bit number

Running N-1 test using base 19

Generic modular reduction using generic reduction AVX-512 FFT length 7K on A 70180-bit number

Running N+1 test using discriminant 29, base 1+sqrt(29)

Generic modular reduction using generic reduction AVX-512 FFT length 7K on A 70180-bit number

Calling N-1 BLS with factored part 0.41% and helper 0.02% (1.27% proof)

1382651896...2487135601 is Fermat and Lucas PRP! (33.6916s+0.0047s)

[Elapsed time: 35.00 seconds]modified 2023-09-17 09:00:41 created 2023-09-17 09:00:01 id 182281

Query times: 0.0002 seconds to select prime, 0.0005 seconds to seek comments.

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