# (2^{253987} - 1)^{2} - 2

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#### This prime's information:

Description: | (2^{253987} - 1)^{2} - 2 |
---|---|

Verification status (*): | Proven |

Official Comment (*): | [none] |

Unofficial Comments: | This prime has 1 user comment below. |

Proof-code(s): (*): | p89 : Emmanuel, OpenPFGW |

Decimal Digits: | 152916 (log_{10} is 152915.41101742) |

Rank (*): | 41486 (digit rank is 1) |

Entrance Rank (*): | 912 |

Currently on list? (*): | no |

Submitted: | 5/7/2007 20:02:47 UTC |

Last modified: | 3/11/2023 15:54:10 UTC |

Removed (*): | 6/3/2010 18:44:26 UTC |

Database id: | 80384 |

Status Flags: | none |

Score (*): | 40.8622 (normalized score 0.0141) |

#### User comments about this prime (disclaimer):

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#### 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 80384 person_id 9 machine RedHat P4 P4 what trial_divided notes Command: /home/caldwell/client/pfgw -o -f -q"(2^253987-1)^2-2" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] trial factoring to 53636202 (2^253987-1)^2-2 has no small factor. [Elapsed time: 611.666 seconds] modified 2020-07-07 22:30:41 created 2007-05-07 20:22:13 id 89880

field value prime_id 80384 person_id 9 machine RedHat P4 P4 what prime notes Command: /home/caldwell/client/pfgw -tc -q"(2^253987-1)^2-2" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing (2^253987-1)^2-2 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 5 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(65536,20) to FFT(65536,19) Reduced from FFT(65536,19) to FFT(65536,18) Reduced from FFT(65536,18) to FFT(65536,17) Reduced from FFT(65536,17) to FFT(65536,16) 1015956 bit request FFT size=(65536,16) Running N+1 test using discriminant 11, base 2+sqrt(11) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(65536,20) to FFT(65536,19) Reduced from FFT(65536,19) to FFT(65536,18) Reduced from FFT(65536,18) to FFT(65536,17) Reduced from FFT(65536,17) to FFT(65536,16) 1015964 bit request FFT size=(65536,16) Running N+1 test using discriminant 11, base 3+sqrt(11) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(65536,20) to FFT(65536,19) Reduced from FFT(65536,19) to FFT(65536,18) Reduced from FFT(65536,18) to FFT(65536,17) Reduced from FFT(65536,17) to FFT(65536,16) 1015964 bit request FFT size=(65536,16) Running N+1 test using discriminant 11, base 4+sqrt(11) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(65536,20) to FFT(65536,19) Reduced from FFT(65536,19) to FFT(65536,18) Reduced from FFT(65536,18) to FFT(65536,17) Reduced from FFT(65536,17) to FFT(65536,16) 1015964 bit request FFT size=(65536,16) Calling N+1 BLS with factored part 50.00% and helper 0.01% (150.02% proof) (2^253987-1)^2-2 is prime! (-1201.8184s+0.0200s) [Elapsed time: 34402 seconds] modified 2020-07-07 22:30:41 created 2007-05-07 20:23:03 id 89881

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

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