# 19540909 · 2^{690774} + 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: | 19540909 · 2^{690774} + 1 |
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Verification status (*): | Proven |

Official Comment (*): | [none] |

Proof-code(s): (*): | g393 : Tamai, NewPGen, PRP, Proth.exe |

Decimal Digits: | 207951 (log_{10} is 207950.98516955) |

Rank (*): | 25547 (digit rank is 1) |

Entrance Rank (*): | 166 |

Currently on list? (*): | no |

Submitted: | 7/6/2005 02:12:34 CDT |

Last modified: | 7/6/2005 02:12:34 CDT |

Removed (*): | 1/25/2012 23:06:53 CDT |

Database id: | 74990 |

Status Flags: | none |

Score (*): | 41.8082 (normalized score 0.0727) |

#### 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 74990 person_id 9 machine Linux P4 2.8GHz what prime notes Command: /home/caldwell/client/pfgw -f -t -q"19540909*2^690774+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 19540909*2^690774+1 [N-1, Brillhart-Lehmer-Selfridge] trial factoring to 74427000 Running N-1 test using base 3 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(98304,20) to FFT(98304,19) Reduced from FFT(98304,19) to FFT(98304,18) Reduced from FFT(98304,18) to FFT(98304,17) Reduced from FFT(98304,17) to FFT(98304,16) 1381606 bit request FFT size=(98304,16) Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 19540909*2^690774+1 is prime! (10115.6308s+0.0006s) modified 2020-07-07 17:30:43 created 2005-07-06 02:23:00 id 80086

Query times: 0.0002 seconds to select prime, 0.0004 seconds to seek comments.

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