# (2^{248949} - 1)^{2} - 2

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: | (2^{248949} - 1)^{2} - 2 |
---|---|

Verification status (*): | Proven |

Official Comment (*): | [none] |

Proof-code(s): (*): | p191 : Rosink, MultiSieve, OpenPFGW |

Decimal Digits: | 149883 (log_{10} is 149882.23278111) |

Rank (*): | 36592 (digit rank is 1) |

Entrance Rank (*): | 552 |

Currently on list? (*): | no |

Submitted: | 3/28/2006 11:18:11 CDT |

Last modified: | 3/29/2006 16:54:21 CDT |

Removed (*): | 4/14/2010 12:44:35 CDT |

Database id: | 77385 |

Status Flags: | none |

Score (*): | 40.8005 (normalized score 0.0258) |

#### 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 77385 person_id 9 machine WinXP Pentium M 1.7GHz what prime notes Command: pfgw.exe -n -tc -q"(2^248949-1)^2-2" 2>&1 PFGW Version 20030811.Win_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Running N-1 test using base 11 Primality testing (2^248949-1)^2-2 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 17, base 1+sqrt(17) Running N+1 test using discriminant 17, base 2+sqrt(17) Running N+1 test using discriminant 17, base 3+sqrt(17) N+1: (2^248949-1)^2-2 460000/4Calling N+1 BLS with factored part 50.08% and helper 0.00% (150.23% proof) (2^248949-1)^2-2 is prime! (100261.9571s+0.1037s) 97899 [Elapsed time: 100257 seconds] modified 2020-07-07 17:30:42 created 2006-03-28 13:03:19 id 83781

field value prime_id 77385 person_id 9 machine Linux P4 2.8GHz what trial_divided notes Command: /home/caldwell/client/pfgw -o -f -q"(2^248949-1)^2-2" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] trial factoring to 52502463 (2^248949-1)^2-2 has no small factor. [Elapsed time: 2114.367 seconds] modified 2020-07-07 17:30:42 created 2006-03-28 18:12:11 id 83790

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

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