# 196597 · 2^{2178109} - 1

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.

Description: | 196597 · 2^{2178109} - 1 |
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Verification status (*): | Proven |

Official Comment (*): | [none] |

Proof-code(s): (*): | L175 : Duggan, ProthSieve, RieselSieve, LLR |

Decimal Digits: | 655682 (log_{10} is 655681.43640256) |

Rank (*): | 2484 (digit rank is 1) |

Entrance Rank (*): | 21 |

Currently on list? (*): | yes |

Submitted: | 5/9/2006 06:01:07 CDT |

Last modified: | 7/7/2006 00:52:23 CDT |

Database id: | 77753 |

Status Flags: | none |

Score (*): | 45.3375 (normalized score 2.408) |

#### 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 77753 person_id 9 machine WinXP P4 2.2GHz M what prime notes Command: pfgw.exe -n -f -tp -q"196597*2^2178109-1" 2>&1 PFGW Version 1.2.0 for Windows [FFT v23.8] Primality testing 196597*2^2178109-1 [N+1, Brillhart-Lehmer-Selfridge] trial factoring to 252181701 Running N+1 test using discriminant 3, base 1+sqrt(3) Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 196597*2^2178109-1 is prime! (264634.1630s+0.0938s) [Elapsed time: 264618 seconds] modified 2020-07-07 17:30:42 created 2006-05-10 11:28:00 id 84294

field value prime_id 77753 person_id 9 machine GenToo P3 400MHz what trial_divided notes Command: /home/caldwell/client/TrialDiv/TrialDiv -q 196597 2 2178109 -1 2>&1 [Elapsed time: 10.116 seconds] modified 2020-07-07 17:30:42 created 2006-07-07 00:52:12 id 84635

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

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