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# Phi(3, - 1833726^{16384})

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: | Phi(3, - 1833726^{16384}) |
---|---|

Verification status (*): | Proven |

Official Comment (*): | Generalized unique |

Proof-code(s): (*): | f6 : Carmody, PhiSieve, PIES, ForEis |

Decimal Digits: | 205237 (log_{10} is 205236.94302155) |

Rank (*): | 24533 (digit rank is 1) |

Entrance Rank (*): | 296 |

Currently on list? (*): | no |

Submitted: | 10/11/2006 14:29:01 CDT |

Last modified: | 10/11/2006 17:09:24 CDT |

Database id: | 78645 |

Status Flags: | none |

Score (*): | 41.7678 (normalized score 0.0852) |

#### Archival tags:

There are certain forms classed as archivable: these prime may (at times) remain on this list even if they do not make the Top 5000 proper. Such primes are tracked with archival tags.

- Generalized Unique (archivable *)
- Prime on list:
no, rank173

Subcategory: "Generalized Unique"

(archival tag id 224249, tag last modified 2020-08-04 13:50:04)

#### 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 78645 person_id 9 machine RedHat P4 P4 what trial_divided notes Command: /home/caldwell/client/pfgw -o -f1{98304} -q"Phi(3,-1833726^16384)" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Factoring numbers to 1% of normal. Using modular factorization: {98304} trial factoring to 13814264571 Phi(3,-1833726^16384) has no small factor. [Elapsed time: 17.426 seconds] modified 2020-07-07 17:30:42 created 2006-10-11 14:52:02 id 86387

field value prime_id 78645 person_id 9 machine RedHat P4 P4 what prime notes Command: /home/caldwell/client/pfgw -t -q"Phi(3,-1833726^16384)" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing Phi(3,-1833726^16384) [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 11 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) 1363574 bit request FFT size=(98304,16) Calling Brillhart-Lehmer-Selfridge with factored part 43.79% Phi(3,-1833726^16384) is prime! (-698.6046s+0.2900s) [Elapsed time: 8183 seconds] modified 2020-07-07 17:30:42 created 2006-10-11 14:53:01 id 86388

Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.

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