# Ramanujan tau function at 199^4518 ECPP

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: | Ramanujan tau function at 199^4518 ECPP |
---|---|

Verification status (*): | PRP |

Official Comment (*): | ECPP |

Proof-code(s): (*): | E3 : Enge, CM |

Decimal Digits: | 57125 (log_{10} is 57124.162537428) |

Rank (*): | 55135 (digit rank is 1) |

Entrance Rank (*): | 54894 |

Currently on list? (*): | short |

Submitted: | 9/9/2022 13:53:05 CDT |

Last modified: | 9/9/2022 14:37:22 CDT |

Database id: | 134371 |

Blob database id: | 442 |

Status Flags: | Reparse, Verify, TrialDiv |

Score (*): | 37.828 (normalized score 0.001) |

#### Description: (from blob table id=442)

[This prime has a pre-calculated decimal expansion (linked blob)]

#### 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, rank1

Subcategory: "ECPP"

(archival tag id 227309, tag last modified 2022-09-09 14:37:23)

#### 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 134371 person_id 9 machine Using: Dual Intel Xeon Gold 5222 CPUs 3.8GHz what prp notes Command: /home/caldwell/clientpool/1/pfgw64 -tc p_134371.txt 2>&1

PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8]

Primality testing 1453909679...7604870201 [N-1/N+1, Brillhart-Lehmer-Selfridge]

Running N-1 test using base 11

Running N+1 test using discriminant 17, base 10+sqrt(17)

Calling N-1 BLS with factored part 0.04% and helper 0.01% (0.15% proof)

1453909679...7604870201 is Fermat and Lucas PRP! (107.9871s+0.0082s)

[Elapsed time: 1.80 minutes]modified 2022-09-09 14:05:49 created 2022-09-09 14:04:01 id 180150

Query times: 0.0003 seconds to select prime, 0.0004 seconds to seek comments.

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