(V(5111, 1, 3789) + 1)/(V(5111, 1, 9) + 1)
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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:(V(5111, 1, 3789) + 1)/(V(5111, 1, 9) + 1)
Verification status (*):PRP
Official Comment:Lehmer primitive part
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):x25 : Water, Broadhurst, Primo, OpenPFGW
Decimal Digits:14019   (log10 is 14018.152167167)
Rank (*):68335 (digit rank is 1)
Entrance Rank (*):58224
Currently on list? (*):short
Submitted:2/10/2013 13:37:23 CDT
Last modified:2/10/2013 13:50:31 CDT
Database id:111175
Status Flags:Verify
Score (*):33.4865 (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.
Lehmer primitive part (archivable *)
Prime on list: yes, rank 14
Subcategory: "Lehmer primitive part"
(archival tag id 215069, tag last modified 2016-06-14 19:50:41)

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 14019 digits 27.02% factorization with details in http://physics.open.ac.uk/~dbroadhu/cert/lh5111.zip and a certificate compressed to 2 MB in http://physics.open.ac.uk/~dbroadhu/cert/lh5111_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_id111175
person_id9
machineDitto P4 P4
whatprp
notesCommand: /home/ditto/client/pfgw -tc -q"(lucasV(5111,1,3789)+1)/(lucasV(5111,1,9)+1)" 2>&1
PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5]
Primality testing (lucasV(5111,1,3789)+1)/(lucasV(5111,1,9)+1) [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 23
Running N+1 test using discriminant 31, base 10+sqrt(31)
Calling N-1 BLS with factored part 2.12% and helper 0.00% (6.37% proof)
(lucasV(5111,1,3789)+1)/(lucasV(5111,1,9)+1) is Fermat and Lucas PRP! (87.7817s+0.0283s)
[Elapsed time: 88.00 seconds]
modified2013-02-16 12:06:20
created2013-02-10 13:38:01
id152624

fieldvalue
prime_id111175
person_id9
machineRedHat P4 P4
whattrial_divided
notesCommand: /home/caldwell/client/pfgw -o -f -q"(lucasV(5111,1,3789)+1)/(lucasV(5111,1,9)+1)" 2>&1
PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5]
(lucasV(5111,1,3....asV(5111,1,9)+1) 1/1 mro=0


trial factoring to 4138045
(lucasV(5111,1,3789)+1)/(lucasV(5111,1,9)+1) has no small factor.
[Elapsed time: 5.120 seconds]
modified2013-02-16 12:06:20
created2013-02-10 13:49:15
id152626

Query times: 0.0005 seconds to select prime, 0.0006 seconds to seek comments.