# 262419 · 2^{262419} + 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: | 262419 · 2^{262419} + 1 |
---|---|

Verification status (*): | Proven |

Official Comment (*): | Cullen |

Proof-code(s): (*): | DS : Smith_Darren, Proth.exe |

Decimal Digits: | 79002 (log_{10} is 79001.409427423) |

Rank (*): | 49070 (digit rank is 1) |

Entrance Rank (*): | 8 |

Currently on list? (*): | short |

Submitted: | 3/8/1998 17:57:01 CDT |

Last modified: | 3/8/1998 17:57:01 CDT |

Database id: | 271 |

Status Flags: | none |

Score (*): | 38.8278 (normalized score 0.0035) |

#### 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.

- Cullen primes (archivable *)
- Prime on list:
yes, rank6

Subcategory: "Cullen primes"

(archival tag id 188565, tag last modified 2009-08-04 21:58:38)

#### 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 271 person_id 9 machine WinXP P4 1.8GHz what prime notes PFGW Version 20021217.Win_Dev (Beta 'caveat utilitor') [FFT v22.7 w/P4] Running N-1 test using base 5 Primality testing 262419*2^262419+1 [N-1, Brillhart-Lehmer-Selfridge] Calling Brillhart-Lehmer-Selfridge with factored part 99.99% 262419*2^262419+1 is prime! (492.016000 seconds) modified 2003-03-25 11:21:48 created 2003-01-22 12:07:28 id 67284

Query times: 0.0004 seconds to select prime, 0.0006 seconds to seek comments.

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