# (30406^{12288} + 698989 · (30406^{8192} + 1))^{2} + 2

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Description: | (30406^{12288} + 698989 · (30406^{8192} + 1))^{2} + 2 |
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Verification status (*): | Proven |

Official Comment (*): | [none] |

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

Proof-code(s): (*): | p192 : Broadhurst, Gallot, Proth.exe, OpenPFGW |

Decimal Digits: | 110174 (log_{10} is 110173.20753973) |

Rank (*): | 42035 (digit rank is 2) |

Entrance Rank (*): | 1166 |

Currently on list? (*): | no |

Submitted: | 4/17/2006 04:16:09 CDT |

Last modified: | 7/7/2006 04:39:47 CDT |

Removed (*): | 3/5/2009 23:46:38 CDT |

Database id: | 77601 |

Status Flags: | none |

Score (*): | 39.8527 (normalized score 0.0098) |

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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 77601 person_id 9 machine WinXP Pent_M 1.7GHz Laptop what prime notes Command: pfgw.exe -n -tc -hhelp.txt -q"(30406^12288+698989*(30406^8192+1))^2+2" 2>&1 PFGW Version 20030811.Win_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Reading factors from helper file help.txt Running N-1 test using base 2 Primality testing (30406^12288+698989*(30406^8192+1))^2+2 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 5, base 1+sqrt(5) Running N+1 test using discriminant 5, base 2+sqrt(5) Running N+1 test using discriminant 5, base 4+sqrt(5) N+1: (30406^12288+698989*(30406^8192+1))^2+2 302500/365988Calling N-1 BLS with factored part 33.34% and helper 0.01% (100.02% proof) (30406^12288+698989*(30406^8192+1))^2+2 is prime! (83631.4790s+0.1958s) [Elapsed time: 83628 seconds] Helper File: 30406^8192+1 modified 2020-07-07 17:30:42 created 2006-04-18 07:28:36 id 84133

field value prime_id 77601 person_id 9 machine GenToo P3 400MHz what trial_divided notes Command: /home/caldwell/client/pfgw -o -f -q"(30406^12288+698989*(30406^8192+1))^2+2" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] trial factoring to 37804219 (30406^12288+698989*(30406^8192+1))^2+2 has no small factor. [Elapsed time: 315.396 seconds] modified 2020-07-07 17:30:42 created 2006-07-07 04:34:32 id 84791

Query times: 0.0005 seconds to select prime, 0.0008 seconds to seek comments.

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