primV(4836, 1, 16704)

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(4836, 1, 16704)
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:39616   (log10 is 39615.596413949)
Rank (*):64975 (digit rank is 1)
Entrance Rank (*):44829
Currently on list? (*):short
Submitted:1/24/2013 00:27:22 UTC
Last modified:3/11/2023 15:54:10 UTC
Database id:110815
Status Flags:Verify
Score (*):36.6984 (normalized score 0.0002)

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 5
Subcategory: "Generalized Lucas primitive part"
(archival tag id 214912, tag last modified 2023-03-11 15:53:59)

User comments about this prime (disclaimer):

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David Broadhurst writes (11 Sep 2014):  (report abuse)
CHG proof at 39616 digits and 27.05% factorization with details in and a certificate compressed to 5 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.
machineRedHat P4 P4
notesCommand: /home/caldwell/client/pfgw -tc -q"primV(4836,1,16704)" 2>&1 PFGW Version [GWNUM 26.5] Primality testing primV(4836,1,16704) [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 23 Running N-1 test using base 37 Running N-1 test using base 47 Running N+1 test using discriminant 67, base 17+sqrt(67) Calling N-1 BLS with factored part 1.14% and helper 0.03% (3.44% proof) primV(4836,1,16704) is Fermat and Lucas PRP! (979.5645s+0.1204s) [Elapsed time: 16.33 minutes]
modified2020-07-07 22:30:23
created2013-01-24 00:29:43

machineDitto P4 P4
notesCommand: /home/ditto/client/pfgw -o -f -q"primV(4836,1,16704)" 2>&1 PFGW Version [GWNUM 26.5] primV(4836,1,16704) 1/1 mro=0 trial factoring to 12651252 primV(4836,1,16704) has no small factor. [Elapsed time: 40.898 seconds]
modified2020-07-07 22:30:23
created2013-01-24 00:35:01

Query times: 0.0003 seconds to select prime, 0.0024 seconds to seek comments.
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