# 2 · 3^{1074726} + 1

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Description: | 2 · 3^{1074726} + 1 |
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Verification status (*): | Proven |

Official Comment (*): | [none] |

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

Proof-code(s): (*): | p199 : Broadhurst, NewPGen, OpenPFGW |

Decimal Digits: | 512775 (log_{10} is 512774.91862984) |

Rank (*): | 4980 (digit rank is 1) |

Entrance Rank (*): | 91 |

Currently on list? (*): | yes |

Submitted: | 2/13/2010 07:52:58 CDT |

Last modified: | 2/17/2010 07:50:50 CDT |

Database id: | 91746 |

Status Flags: | none |

Score (*): | 44.5826 (normalized score 1.0032) |

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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 91746 person_id 9 machine RedHat P4 P4 what prime notes Command: /home/caldwell/client/pfgw -t -q"2*3^1074726+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 2*3^1074726+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(229376,19) to FFT(229376,18) Reduced from FFT(229376,18) to FFT(229376,17) Reduced from FFT(229376,17) to FFT(229376,16) 3406812 bit request FFT size=(229376,16) Running N-1 test using base 3 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(229376,19) to FFT(229376,18) Reduced from FFT(229376,18) to FFT(229376,17) Reduced from FFT(229376,17) to FFT(229376,16) 3406812 bit request FFT size=(229376,16) Running N-1 test using base 17 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(229376,19) to FFT(229376,18) Reduced from FFT(229376,18) to FFT(229376,17) Reduced from FFT(229376,17) to FFT(229376,16) 3406812 bit request FFT size=(229376,16) Running N-1 test using base 23 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(229376,19) to FFT(229376,18) Reduced from FFT(229376,18) to FFT(229376,17) Reduced from FFT(229376,17) to FFT(229376,16) 3406812 bit request FFT size=(229376,16) Running N-1 test using base 29 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(229376,19) to FFT(229376,18) Reduced from FFT(229376,18) to FFT(229376,17) Reduced from FFT(229376,17) to FFT(229376,16) 3406812 bit request FFT size=(229376,16) Running N-1 test using base 31 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(229376,19) to FFT(229376,18) Reduced from FFT(229376,18) to FFT(229376,17) Reduced from FFT(229376,17) to FFT(229376,16) 3406812 bit request FFT size=(229376,16) Running N-1 test using base 41 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(229376,19) to FFT(229376,18) Reduced from FFT(229376,18) to FFT(229376,17) Reduced from FFT(229376,17) to FFT(229376,16) 3406812 bit request FFT size=(229376,16) Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 2*3^1074726+1 is prime! (-1665.4337s+0.1400s) [Elapsed time: 4.00 days] modified 2020-07-07 17:30:36 created 2010-02-13 07:53:01 id 112867

field value prime_id 91746 person_id 9 machine Ditto P4 P4 what trial_divided notes Command: /home/ditto/client/TrialDiv/TrialDiv -q 2 3 1074726 1 2>&1 [Elapsed time: 10.060 seconds] modified 2020-07-07 17:30:36 created 2010-02-13 08:05:02 id 112868

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

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