(V(3755, 1, 3753) - 1)/(V(3755, 1, 27) - 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(3755, 1, 3753) - 1)/(V(3755, 1, 27) - 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:13319   (log10 is 13318.996526669)
Rank (*):70303 (digit rank is 1)
Entrance Rank (*):49669
Currently on list? (*):short
Submitted:5/21/2011 07:26:04 CDT
Last modified:5/21/2011 07:50:24 CDT
Database id:100144
Status Flags:Verify
Score (*):33.328 (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 20
Subcategory: "Lehmer primitive part"
(archival tag id 213243, 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 26.98%

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"(lucasV(3755,1,3753)-1)/(lucasV(3755,1,27)-1)" 2>&1
PFGW Version [GWNUM 25.14]
Primality testing (lucasV(3755,1,3753)-1)/(lucasV(3755,1,27)-1) [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 7
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 0.01% (6.37% proof)
(lucasV(3755,1,3753)-1)/(lucasV(3755,1,27)-1) is Fermat and Lucas PRP! (56.0603s+0.0091s)
[Elapsed time: 60.00 seconds]
modified2011-12-27 16:48:33
created2011-05-21 07:27:39

machineDitto P4 P4
notesCommand: /home/ditto/client/pfgw -o -f -q"(lucasV(3755,1,3753)-1)/(lucasV(3755,1,27)-1)" 2>&1
PFGW Version [GWNUM 26.5]
(lucasV(3755,1,3....sV(3755,1,27)-1) 1/1 mro=0

trial factoring to 3915771
(lucasV(3755,1,3753)-1)/(lucasV(3755,1,27)-1) has no small factor.
[Elapsed time: 4.581 seconds]
modified2011-12-27 16:48:33
created2011-05-21 07:35:01

Query times: 0.0007 seconds to select prime, 0.0008 seconds to seek comments.