11 · 22691961 + 1

At this site we maintain a list of the 5000 Largest Known Primes which is updated hourly.  This list is the most important PrimePages database: a collection of research, records and results all about prime numbers. This page summarizes our information about one of these primes.

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 (*):2124 (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 4.092)

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 8, weight 48.385653311462
Subcategory: "Divides GF(*,12)"
(archival tag id 215198, tag last modified 2022-04-12 17:37:10)

User comments about this prime (disclaimer):

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Serge Batalov writes (11 Sep 2014):  (report abuse)
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.
machineRedHat P4 P4
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 11 2 2691961 1 2>&1 [Elapsed time: 10.315 seconds]
modified2020-07-07 17:30:22
created2013-03-05 00:48:01

machineRedHat P4 P4
notesCommand: /home/caldwell/client/pfgw -t -q"11*2^2691961+1" 2>&1 PFGW Version [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]
modified2020-07-07 17:30:22
created2013-03-05 00:53:01

Query times: 0.0004 seconds to select prime, 0.0005 seconds to seek comments.
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