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# 2^{216091} - 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: | 2^{216091} - 1 |
---|---|

Verification status (*): | Proven |

Official Comment (*): | Mersenne 31 |

Proof-code(s): (*): | S : Slowinski |

Decimal Digits: | 65050 (log_{10} is 65049.8727930254) |

Rank (*): | 49709 (digit rank is 1) |

Entrance Rank (*): | 1 |

Currently on list? (*): | no |

Submitted: | 9/6/1985 |

Last modified: | 9/6/1985 |

Database id: | 392 |

Status Flags: | none |

Score (*): | 38.2287 (normalized score 0.0024) |

#### 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.

#### 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 392 person_id 9 machine RedHat P4 P4 what prime notes Command: /home/caldwell/client/pfgw -tp -q"2^216091-1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 2^216091-1 [N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 3, base 1+sqrt(3) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(28672,20) to FFT(28672,19) Reduced from FFT(28672,19) to FFT(28672,18) Reduced from FFT(28672,18) to FFT(28672,17) Reduced from FFT(28672,17) to FFT(28672,16) 432198 bit request FFT size=(28672,16) Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 2^216091-1 is prime! (621.0900s+0.0000s) [Elapsed time: 10.37 minutes] modified 2020-07-07 17:30:39 created 2008-08-05 21:03:43 id 100211

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

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