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: 1638535589 · 16001#/5+1 Verification status (*): Proven Official Comment: Arithmetic progression (5,d=2003735*16001#) Proof-code(s): (*): p199 : Broadhurst, NewPGen, OpenPFGW Decimal Digits: 6913   (log10 is 6912.2659371771) Rank (*): 48371 (digit rank is 8) Entrance Rank (*): 42946 Currently on list? (*): short Submitted: 6/26/2008 19:53:45 CDT Last modified: 6/26/2008 20:20:25 CDT Database id: 85236 Status Flags: none Score (*): 31.2948 (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: yes, rank 4, weight 46.135462037046
Subcategory: "Arithmetic progression (5,d=*)"
(archival tag id 194756, tag last modified 2009-03-04 03:50:22)

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 85236 person_id 9 machine Ditto P4 P4 what trial_divided notes Command: /home/ditto/client/pfgw -o -f -q"1638535589*16001#/5+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] trial factoring to 1926812 1638535589*16001#/5+1 has no small factor. [Ellapsed time: 1.248 seconds] modified 2008-07-08 09:36:29 created 2008-06-26 20:05:07 id 99728

field value prime_id 85236 person_id 9 machine Ditto P4 P4 what prime notes Command: /home/ditto/client/pfgw -t -q"1638535589*16001#/5+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 1638535589*16001#/5+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(3072,21) to FFT(3072,20) Reduced from FFT(3072,20) to FFT(3072,19) Reduced from FFT(3072,19) to FFT(3072,18) Reduced from FFT(3072,18) to FFT(3072,17) Reduced from FFT(3072,17) to FFT(3072,16) 45934 bit request FFT size=(3072,16) Calling Brillhart-Lehmer-Selfridge with factored part 33.39% 1638535589*16001#/5+1 is prime! (33.7300s+0.0000s) [Elapsed time: 34.00 seconds] modified 2008-07-08 09:36:29 created 2008-06-26 20:10:26 id 99733