# (84055657369 · 205881 · 4001# · (205881 · 4001# + 1) + 210) · (205881 · 4001# - 1)/35 + 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.

#### This prime's information:

Description: | (84055657369 · 205881 · 4001# · (205881 · 4001# + 1) + 210) · (205881 · 4001# - 1)/35 + 1 |
---|---|

Verification status (*): | Proven |

Official Comment (*): | Consecutive primes arithmetic progression (1,d=6) |

Proof-code(s): (*): | p179 : DavisK, APTreeSieve, OpenPFGW |

Decimal Digits: | 5132 (log_{10} is 5131.89444824) |

Rank (*): | 89315 (digit rank is 9) |

Entrance Rank (*): | 38380 |

Currently on list? (*): | no |

Submitted: | 4/1/2006 12:26:30 UTC |

Last modified: | 3/11/2023 15:54:10 UTC |

Database id: | 77460 |

Status Flags: | none |

Score (*): | 30.37 (normalized score 0) |

#### 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.

- Arithmetic Progressions of Primes (archivable class *)
- Prime on list:
no, rank294

Subcategory: "Arithmetic progression (1,d=*)"

(archival tag id 195102, tag last modified 2023-03-11 15:53:59)- Consecutive Primes in Arithmetic Progression (archivable class *)
- Prime on list:
no, rank20

Subcategory: "Consecutive primes in arithmetic progression (1,d=*)"

(archival tag id 195101, tag last modified 2023-03-11 15:53:59)

#### 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 77460 person_id 9 machine GenToo P3 400MHz what prime notes PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing (84055657369*205881*4001#*(205881*4001#+1)+210)*(205881*4001#-1)/35+1 [N-1, Brillhart-Lehmer-Selfridge] Reading factors from helper file helper_file_id_77460 Running N-1 test using base 5 Using non-SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(2048,22) to FFT(2048,21) Reduced from FFT(2048,21) to FFT(2048,20) Reduced from FFT(2048,20) to FFT(2048,19) Reduced from FFT(2048,19) to FFT(2048,18) Reduced from FFT(2048,18) to FFT(2048,17) 34104 bit request FFT size=(2048,17) Calling Brillhart-Lehmer-Selfridge with factored part 33.34% (84055657369*205881*4001#*(205881*4001#+1)+210)*(205881*4001#-1)/35+1 is prime! (34.7000s+0.0100s) [Elapsed time: 36 seconds] Helper file contains: "205881*4001#-1" modified 2020-07-07 22:30:42 created 2006-04-04 13:24:53 id 83989

field value prime_id 77460 person_id 9 machine GenToo P3 400MHz what trial_divided notes Command: /home/caldwell/client/pfgw -o -f -q"(84055657369*205881*4001#*(205881*4001#+1)+210)*(205881*4001#-1)/35+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] (84055657369*205881*4001#.........10)*(205881*4001 1/1 trial factoring to 1394925 (84055657369*205881*4001#*(205881*4001#+1)+210)*(205881*4001#-1)/35+1 has no small factor. [Elapsed time: 0.716 seconds] modified 2020-07-07 22:30:42 created 2006-07-07 15:40:35 id 85248

Query times: 0.0002 seconds to select prime, 0.0005 seconds to seek comments.

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