6679881 · 26679881 + 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:6679881 · 26679881 + 1
Verification status (*):External
Official Comment:Cullen
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):L917 : Bergman1, Gcwsieve, MultiSieve, PrimeGrid, LLR
Decimal Digits:2010852   (log10 is 2010851.37323463)
Rank (*):26 (digit rank is 1)
Entrance Rank (*):15
Currently on list? (*):short
Submitted:8/4/2009 21:37:30 CDT
Last modified:8/4/2009 22:42:38 CDT
Database id:89536
Status Flags:none
Score (*):48.7752 (normalized score 201.7915)

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.
Cullen primes (archivable *)
Prime on list: yes, rank 1
Subcategory: "Cullen primes"
(archival tag id 210484, tag last modified 2009-08-04 21:58:38)

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.

PrimeGrid writes (11 Sep 2014): 
For more information, please see the Official Announcement.

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_id89536
person_id9
machineRedHat P4 P4
whattrial_divided
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 6679881 2 6679881 1 2>&1
[Elapsed time: 14.014 seconds]
modified2011-12-27 16:48:42
created2009-08-04 21:48:02
id108443

fieldvalue
prime_id89536
person_id9
machineExternal
whatprime
notesNotes from PrimeGrid:
Hardware:
LLR 3.7.1c: Intel(R) Xeon(R) CPU L5420 @ 2.50GHz running Microsoft Windows XP Professional x64 Edition
run time: 259,106.72 seconds
LLR 3.7.1c: Intel(R) Core(TM)2 Duo CPU E6750 @ 2.66GHz running Microsoft Windows XP Professional x86 Edition
run time: 121,878.88 seconds
As with all primes from PrimeGrid, we require two (2) matching LLR results before primality is proven.
A third primality test was run using the following:
PFGW 3.2: Intel(R) Core(TM)2 Extreme CPU Q6850 @ 3.00GHz running Ubuntu 7.10
Primality testing 6679881*2^6679881+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%
6679881*2^6679881+1 is prime! (120687.9084s+0.0485s)
modified2009-11-24 13:57:52
created2009-08-04 21:38:01
id108442

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