# (14665 · 10^{34110} - 56641)/9999

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: | (14665 · 10^{34110} - 56641)/9999 |
---|---|

Verification status (*): | PRP |

Official Comment (*): | ECPP, Palindrome |

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

Proof-code(s): (*): | c89 : Broadhurst, Underwood, Primo |

Decimal Digits: | 34111 (log_{10} is 34110.166325499) |

Rank (*): | 62844 (digit rank is 1) |

Entrance Rank (*): | 57092 |

Currently on list? (*): | short |

Submitted: | 3/29/2018 17:38:40 CDT |

Last modified: | 3/29/2018 19:20:12 CDT |

Database id: | 124558 |

Status Flags: | Verify, TrialDiv |

Score (*): | 36.2364 (normalized score 0.0002) |

#### 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.

- Elliptic Curve Primality Proof (archivable *)
- Prime on list:
yes, rank12

Subcategory: "ECPP"

(archival tag id 219093, tag last modified 2022-09-09 14:37:23)- Palindrome (archivable *)
- Prime on list:
no, rank165

Subcategory: "Palindrome"

(archival tag id 219094, tag last modified 2021-10-22 20:37:57)

#### 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 124558 person_id 9 machine Using: Xeon 4c+4c 3.5GHz what prp notes Command: /home/caldwell/client/pfgw/pfgw64 -tc -q"(14665*10^34110-56641)/9999" 2>&1 PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing (14665*10^34110-56641)/9999 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 11 Running N+1 test using discriminant 19, base 15+sqrt(19) Calling N-1 BLS with factored part 0.03% and helper 0.03% (0.14% proof) (14665*10^34110-56641)/9999 is Fermat and Lucas PRP! (94.7432s+0.0007s) [Elapsed time: 1.58 minutes] modified 2020-07-07 17:30:15 created 2018-03-29 17:41:01 id 170223

Query times: 0.0003 seconds to select prime, 0.0005 seconds to seek comments.

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