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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
Verification status (*):PRP
Official Comment:Lucas cofactor, ECPP
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):c4 : Broadhurst, Primo
Decimal Digits:5803   (log10 is 5802.9452332826)
Rank (*):80236 (digit rank is 1)
Entrance Rank (*):61729
Currently on list? (*):short
Submitted:11/20/2011 18:23:49 CDT
Last modified:11/20/2011 18:50:25 CDT
Database id:103243
Status Flags:Verify
Score (*):30.7517 (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.
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 354
Subcategory: "ECPP"
(archival tag id 213649, tag last modified 2018-06-17 18:50:23)
Lucas cofactor (archivable *)
Prime on list: yes, rank 17
Subcategory: "Lucas cofactor"
(archival tag id 213650, tag last modified 2015-03-12 17:20:33)

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): 

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.
machineRedHat Virtual STEM Server
notesCommand: /home/caldwell/client/pfgw -tc -q"V(27827)/3579579016301" 2>&1
PFGW Version [GWNUM 25.14]
Primality testing V(27827)/3579579016301 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2
Running N+1 test using discriminant 7, base 2+sqrt(7)
Calling N-1 BLS with factored part 0.10% and helper 0.07% (0.37% proof)
V(27827)/3579579016301 is Fermat and Lucas PRP! (6.6563s+0.0134s)
[Elapsed time: 7.00 seconds]
modified2011-12-27 16:48:26
created2011-11-20 18:26:56

machineDitto P4 P4
notesCommand: /home/ditto/client/pfgw -o -f -q"V(27827)/3579579016301" 2>&1
PFGW Version [GWNUM 26.5]
V(27827)/3579579016301 1/1 mro=0

trial factoring to 1593900
V(27827)/3579579016301 has no small factor.
[Elapsed time: 0.887 seconds]
modified2011-12-27 16:48:26
created2011-11-20 18:35:02

Query times: 0.0005 seconds to select prime, 0.0003 seconds to seek comments.