3 · 27033641 + 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:3 · 27033641 + 1
Verification status (*):Proven
Official Comment (*):Divides GF(7033639,3)
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):L2233 : Herder, Srsieve, PrimeGrid, LLR
Decimal Digits:2117338   (log10 is 2117337.3968532)
Rank (*):241 (digit rank is 1)
Entrance Rank (*):14
Currently on list? (*):short
Submitted:2/28/2011 20:41:20 UTC
Last modified:3/11/2023 15:54:10 UTC
Database id:98959
Status Flags:none
Score (*):48.9334 (normalized score 50.0074)

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 7, weight 50.032067543444
Subcategory: "Divides GF(*,3)"
(archival tag id 213161, tag last modified 2023-03-31 00:37:44)

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):  (report abuse)
3*2^7033641+1 Divides GF(7033639,3)
3*2^7033641+1 Divides GF(7033639,8)
3*2^7033641+1 Divides xGF(7033640,5,2)
3*2^7033641+1 Divides xGF(7033640,6,5)
3*2^7033641+1 Divides xGF(7033639,7,4)
3*2^7033641+1 Divides xGF(7033637,8,3)
3*2^7033641+1 Divides xGF(7033639,9,8)
3*2^7033641+1 Divides xGF(7033640,10,7)
3*2^7033641+1 Divides xGF(7033640,11,4)
3*2^7033641+1 Divides xGF(7033640,11,7)
3*2^7033641+1 Divides xGF(7033638,11,10)
3*2^7033641+1 Divides xGF(7033638,12,7)
3*2^7033641+1 Divides xGF(7033640,12,11)

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.
machineRedHat Virtual STEM Server
notesCommand: /home/caldwell/client/pfgw -t -q"3*2^7033641+1" 2>&1 PFGW Version [GWNUM 25.14] Primality testing 3*2^7033641+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 5 Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 3*2^7033641+1 is prime! (57160.1453s+0.0399s) [Elapsed time: 15.88 hours]
modified2020-07-07 22:30:32
created2011-02-28 20:43:17

machineRedHat P4 P4
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 3 2 7033641 1 2>&1 [Elapsed time: 10.893 seconds]
modified2020-07-07 22:30:32
created2011-02-28 20:48:02

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