At this site we maintain a list of the 5000 Largest Known Primes which is updated hourly. This list is the most important databases at The Prime Pages: 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:

field (help) value Description: (84055657369 · 205881 · 4001# · (205881 · 4001#+1)+210) · (205881 · 4001#-1)/35+13 Verification status (*): Proven Official Comment: Consecutive primes arithmetic progression (3,d=6) Proof-code(s): (*): p179 : DavisK, APTreeSieve, OpenPFGW Decimal Digits: 5132   (log10 is 5131.89444824) Rank (*): 51289 (digit rank is 7) Entrance Rank (*): 38381 Currently on list? (*): short Submitted: 4/1/2006 06:26:32 CDT Last modified: 7/7/2006 10:40:38 CDT Database id: 77462 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, rank 101, weight 35.6129171138249
Subcategory: "Arithmetic progression (3,d=*)"
(archival tag id 195098, tag last modified 2009-03-04 03:50:22)

Consecutive Primes in Arithmetic Progression (archivable class *)

Prime on list: yes, rank 4
Subcategory: "Consecutive primes in arithmetic progression (3,d=*)"
(archival tag id 195097, tag last modified 2009-02-12 20:01:27)

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 77462 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+13" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] (84055657369*205881*4001#.........0)*(205881*4001# 1/1 trial factoring to 1394925 (84055657369*205881*4001#*(205881*4001#+1)+210)*(205881*4001#-1)/35+13 has no small factor. [Elapsed time: 0.708 seconds] modified 2006-07-14 06:27:03 created 2006-07-07 10:40:37 id 85250

field value prime_id 77462 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+13 [N-1/N+1, Brillhart-Lehmer-Selfridge] Reading factors from helper file helper_file_id_77462 Running N-1 test using base 2 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) Running N+1 test using discriminant 7, base 1+sqrt(7) 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) 34112 bit request FFT size=(2048,17) Calling N-1 BLS with factored part 33.41% and helper 0.02% (100.25% proof) (84055657369*205881*4001#*(205881*4001#+1)+210)*(205881*4001#-1)/35+13 is prime! (112.3464s+0.0042s) [Elapsed time: 113 seconds] Helper file contains: "205881*4001#+1" modified 2006-04-04 08:27:44 created 2006-04-04 08:25:51 id 83990