# primV(180906)

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: | primV(180906) |
---|---|

Verification status (*): | PRP |

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

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

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

Decimal Digits: | 22905 (log_{10} is 22904.987572087) |

Rank (*): | 73098 (digit rank is 1) |

Entrance Rank (*): | 73049 |

Currently on list? (*): | short |

Submitted: | 9/30/2024 22:12:27 UTC |

Last modified: | 9/30/2024 23:37:10 UTC |

Database id: | 138595 |

Status Flags: | Verify |

Score (*): | 35.0057 (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 primitive part (archivable *)
- Prime on list:
yes, rank7

Subcategory: "Lucas primitive part"

(archival tag id 229665, tag last modified 2024-10-11 22:37:11)- Elliptic Curve Primality Proof (archivable *)
- Prime on list:
no, rank82

Subcategory: "ECPP"

(archival tag id 229666, tag last modified 2024-10-11 22:37:10)

#### User comments about this prime (disclaimer):

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#### 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 138595 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 9717892427...6288988001 [N-1/N+1, Brillhart-Lehmer-Selfridge]

trial

Running N-1 test using base 17

Generic modular reduction using generic reduction AVX-512 FFT length 7680 on A 76089-bit number

Running N-1 test using base 29

Generic modular reduction using generic reduction AVX-512 FFT length 7680 on A 76089-bit number

Running N+1 test using discriminant 53, base 6+sqrt(53)

Generic modular reduction using generic reduction AVX-512 FFT length 7680 on A 76089-bit number

Calling N-1 BLS with factored part 0.31% and helper 0.01% (0.94% proof)

9717892427...6288988001 is Fermat and Lucas PRP! (25.3595s+0.0047s)

[Elapsed time: 30.00 seconds]modified 2024-09-30 22:41:24 created 2024-09-30 22:40:49 id 184439

Query times: 0.0043 seconds to select prime, 0.0005 seconds to seek comments.

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