primV(6586, 1, 16200)

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:primV(6586, 1, 16200)
Verification status (*):PRP
Official Comment (*):Generalized Lucas primitive part
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):x25 : Broadhurst, Water, OpenPFGW, Primo
Decimal Digits:32993   (log10 is 32992.89162938)
Rank (*):66703 (digit rank is 1)
Entrance Rank (*):46421
Currently on list? (*):short
Submitted:1/13/2013 11:19:48 UTC
Last modified:3/11/2023 15:54:10 UTC
Database id:110705
Status Flags:Verify
Score (*):36.1335 (normalized score 0.0001)

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.
Generalized Lucas primitive part (archivable *)
Prime on list: yes, rank 8
Subcategory: "Generalized Lucas primitive part"
(archival tag id 214907, tag last modified 2023-03-11 15:53:59)

User comments about this prime (disclaimer):

User comments are allowed to convey mathematical information about this number, how it was proven prime.... See our guidelines and restrictions.

David Broadhurst writes (11 Sep 2014):  (report abuse)

CHG proof at 32993 digits and 26.46% factorization with details in and a certificate compressed to 13 MB in

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.
machineDitto P4 P4
notesCommand: /home/ditto/client/pfgw -tc -q"primV(6586,1,16200)" 2>&1 PFGW Version [GWNUM 26.5] Primality testing primV(6586,1,16200) [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 43 Running N+1 test using discriminant 67, base 14+sqrt(67) Calling N-1 BLS with factored part 1.60% and helper 0.04% (4.85% proof) primV(6586,1,16200) is Fermat and Lucas PRP! (514.7202s+0.2471s) [Elapsed time: 8.58 minutes]
modified2020-07-07 22:30:23
created2013-01-13 11:27:29

machineDitto P4 P4
notesCommand: /home/ditto/client/pfgw -o -f -q"primV(6586,1,16200)" 2>&1 PFGW Version [GWNUM 26.5] primV(6586,1,16200) 1/1 mro=0 trial factoring to 10395960 primV(6586,1,16200) has no small factor. [Elapsed time: 35.912 seconds]
modified2020-07-07 22:30:23
created2013-01-13 11:35:02

Query times: 0.0002 seconds to select prime, 0.0004 seconds to seek comments.
Printed from the PrimePages <> © Reginald McLean.