11 · 22230369 + 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.

This prime's information:

Description: 11 · 22230369 + 1 Proven Divides GF(2230368,3) This prime has 1 user comment below. L2561 : Vinklat, PSieve, Srsieve, PrimeGrid, LLR 671410   (log10 is 671409.01179176) 2887 (digit rank is 1) 76 short 9/10/2011 18:51:29 CDT 9/11/2011 09:20:03 CDT 101924 none 45.4103 (normalized score 2.2095)

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 15, weight 47.808232710165
Subcategory: "Divides GF(*,3)"
(archival tag id 213434, tag last modified 2021-02-26 11:20:20)

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PrimeGrid writes (11 Sep 2014):  (report abuse)
 11*2^2230369+1 is a Factor of GF(2230368,3)!!!! 11*2^2230369+1 is a Factor of xGF(2230368,8,5)!!!! 11*2^2230369+1 is a Factor of xGF(2230367,11,4)!!!! 11*2^2230369+1 is a Factor of xGF(2230368,12,11)!!!!

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_id101924
person_id9
machineRedHat P4 P4
whattrial_divided
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 11 2 2230369 1 2>&1 [Elapsed time: 9.914 seconds]
modified2020-07-07 17:30:30
created2011-09-10 18:52:01
id133413

fieldvalue
prime_id101924
person_id9
machineRedHat P4 P4
whatprime
notesCommand: /home/caldwell/client/pfgw -t -q"11*2^2230369+1" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing 11*2^2230369+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 11*2^2230369+1 is prime! (9386.8403s+0.0016s) [Elapsed time: 2.61 hours]
modified2020-07-07 17:30:30
created2011-09-10 18:53:02
id133415

Query times: 0.0003 seconds to select prime, 0.0005 seconds to seek comments.