(133206997 - 1)/13319
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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:(133206997 - 1)/13319
Verification status (*):PRP
Official Comment:Generalized repunit
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):x14 : Steward, Primo, OpenPFGW
Decimal Digits:28856   (log10 is 28855.031589547)
Rank (*):61128 (digit rank is 1)
Entrance Rank (*):36315
Currently on list? (*):no
Submitted:10/15/2010 13:36:31 CDT
Last modified:3/22/2011 18:18:26 CDT
Database id:95420
Status Flags:Verify
Score (*):35.7195 (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 Repunit (archivable *)
Prime on list: no, rank 23
Subcategory: "Generalized Repunit"
(archival tag id 210856, tag last modified 2018-01-24 23:20:10)

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.

Andrew A. D. Steward writes (11 Sep 2014): 
Certificate at http://www.primes.viner-steward.org/andy/W/34081B55.html

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 -o -f -q"(13320^6997-1)/13319" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
trial factoring to 9002185
(13320^6997-1)/13319 has no small factor.
[Elapsed time: 21.834 seconds]
modified2011-12-27 16:48:37
created2010-10-15 13:48:01

machineRedHat P4 P4
notesCommand: /home/caldwell/client/pfgw -tc -q"(13320^6997-1)/13319" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing (13320^6997-1)/13319 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 17
Running N+1 test using discriminant 47, base 8+sqrt(47)
Calling N-1 BLS with factored part 0.44% and helper 0.03% (1.35% proof)
(13320^6997-1)/13319 is Fermat and Lucas PRP! (410.0800s+0.0000s)
[Elapsed time: 6.95 minutes]
modified2010-11-28 11:14:57
created2010-10-15 13:40:19

Query times: 0.0004 seconds to select prime, 0.0003 seconds to seek comments.