11 · 22691961 + 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:11 · 22691961 + 1
Verification status (*):Proven
Official Comment:Divides GF(2691960,12)
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):p286 : Batalov, Srsieve, OpenPFGW
Decimal Digits:810363   (log10 is 810362.04955029)
Rank (*):496 (digit rank is 1)
Entrance Rank (*):95
Currently on list? (*):short
Submitted:3/5/2013 00:41:17 CDT
Last modified:3/5/2013 15:20:03 CDT
Database id:111488
Status Flags:none
Score (*):45.9877 (normalized score 9.2959)

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 Fermat Divisors (bases 3,5,6,10,12) (archivable *)
Prime on list: yes, rank 2, weight 48.3856533114618
Subcategory: "Divides GF(*,12)"
(archival tag id 215198, tag last modified 2016-03-15 13:57:15)

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.

Serge Batalov writes (11 Sep 2014): 
Divides xGF(2691959,7,2), xGF(2691954,11,8), and GF(2691960,12)

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_id111488
person_id9
machineRedHat P4 P4
whattrial_divided
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 11 2 2691961 1 2>&1
[Elapsed time: 10.315 seconds]
modified2013-03-21 09:38:26
created2013-03-05 00:48:01
id153298

fieldvalue
prime_id111488
person_id9
machineRedHat P4 P4
whatprime
notesCommand: /home/caldwell/client/pfgw -t -q"11*2^2691961+1" 2>&1
PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5]
Primality testing 11*2^2691961+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%
11*2^2691961+1 is prime! (15149.3712s+0.0018s)
[Elapsed time: 4.21 hours]
modified2013-03-21 09:38:26
created2013-03-05 00:53:01
id153299

Query times: 0.0004 seconds to select prime, 0.0007 seconds to seek comments.