# 228188^{131072} + 1

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: | 228188^{131072} + 1 |
---|---|

Verification status (*): | Proven |

Official Comment (*): | Generalized Fermat |

Proof-code(s): (*): | g124 : Crickman, Proth.exe |

Decimal Digits: | 702323 (log_{10} is 702322.154132) |

Rank (*): | 2169 (digit rank is 1) |

Entrance Rank (*): | 56 |

Currently on list? (*): | yes |

Submitted: | 8/19/2010 19:25:08 CDT |

Last modified: | 8/20/2010 23:50:29 CDT |

Database id: | 94353 |

Status Flags: | none |

Score (*): | 45.5485 (normalized score 3.0139) |

#### 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 Fermat (archivable *)
- Prime on list:
no, rank527

Subcategory: "Generalized Fermat"

(archival tag id 210831, tag last modified 2021-10-22 02:37:18)

#### 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 94353 person_id 9 machine Ditto P4 P4 what trial_divided notes Command: /home/ditto/client/TrialDiv/TrialDiv -q 1 228188 131072 1 2>&1 [Elapsed time: 8.063 seconds] modified 2020-07-07 17:30:33 created 2010-08-19 19:35:01 id 118088

field value prime_id 94353 person_id 9 machine Ditto P4 P4 what prime notes Command: /home/ditto/client/pfgw -t -q"228188^131072+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 228188^131072+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(327680,19) to FFT(327680,18) Reduced from FFT(327680,18) to FFT(327680,17) Reduced from FFT(327680,17) to FFT(327680,16) 4666136 bit request FFT size=(327680,16) Calling Brillhart-Lehmer-Selfridge with factored part 88.76% 228188^131072+1 is prime! (99736.9294s+0.1414s) [Elapsed time: 27.70 hours] modified 2020-07-07 17:30:33 created 2010-08-19 19:38:02 id 118089

Query times: 0.0004 seconds to select prime, 0.0003 seconds to seek comments.

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