primV(4836, 1, 16704)
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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
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 : Water, Broadhurst, Primo, OpenPFGW
Decimal Digits:39616   (log10 is 39615.596413949)
Rank (*):55060 (digit rank is 1)
Entrance Rank (*):44829
Currently on list? (*):short
Submitted:1/23/2013 18:27:22 CDT
Last modified:1/23/2013 18:50:30 CDT
Database id:110815
Status Flags:Verify
Score (*):36.6984 (normalized score 0.0008)

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 2013-11-15 08:21:24)

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): 
CHG proof at 39616 digits and 27.05% factorization with details in http://physics.open.ac.uk/~dbroadhu/cert/b16704.zip and a certificate compressed to 5 MB in http://physics.open.ac.uk/~dbroadhu/cert/b16704_cert.gp.gz

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.
fieldvalue
prime_id110815
person_id9
machineRedHat P4 P4
whatprp
notesCommand: /home/caldwell/client/pfgw -tc -q"primV(4836,1,16704)" 2>&1
PFGW Version 3.4.5.32BIT.20110215.x86_Dev [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]
modified2013-02-02 20:51:49
created2013-01-23 18:29:43
id151905

fieldvalue
prime_id110815
person_id9
machineDitto P4 P4
whattrial_divided
notesCommand: /home/ditto/client/pfgw -o -f -q"primV(4836,1,16704)" 2>&1
PFGW Version 3.4.5.32BIT.20110215.x86_Dev [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]
modified2013-02-02 20:51:49
created2013-01-23 18:35:01
id151906

Query times: 0.0004 seconds to select prime, 0.0005 seconds to seek comments.