3 · 21832496 + 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:3 · 21832496 + 1
Verification status (*):Proven
Official Comment (*):Divides GF(1832490,3), GF(1832494,5)
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):p189 : Bohanon, LLR, OpenPFGW
Decimal Digits:551637   (log10 is 551636.74005552)
Rank (*):2435 (digit rank is 1)
Entrance Rank (*):43
Currently on list? (*):short
Submitted:7/27/2007 17:17:39 CDT
Last modified:7/28/2007 18:38:30 CDT
Database id:81819
Status Flags:none
Score (*):44.8069 (normalized score 1.8376)

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 12, weight 45.9055999681661
Subcategory: "Divides GF(*,5)"
(archival tag id 187045, tag last modified 2020-06-05 01:20:25)
Generalized Fermat Divisors (bases 3,5,6,10,12) (archivable *)
Prime on list: yes, rank 16, weight 45.9055999681661
Subcategory: "Divides GF(*,3)"
(archival tag id 187044, tag last modified 2020-04-02 19:50:05)

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.

Joseph Bohanon writes (11 Sep 2014):  (report abuse)
This prime also divides GF(1832494,7) and GF(1832495,11).

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_id81819
person_id9
machineRedHat P4 P4
whattrial_divided
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 3 2 1832496 1 2>&1 [Elapsed time: 10.549 seconds]
modified2020-07-07 17:30:41
created2007-07-27 17:22:01
id92754

fieldvalue
prime_id81819
person_id9
machineRedHat P4 P4
whatprime
notesCommand: /home/caldwell/client/pfgw -t -q"3*2^1832496+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 3*2^1832496+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 11 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(229376,19) to FFT(229376,18) Reduced from FFT(229376,18) to FFT(229376,17) Reduced from FFT(229376,17) to FFT(229376,16) 3665004 bit request FFT size=(229376,16) Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 3*2^1832496+1 is prime! (-1118.7865s+0.0000s) [Elapsed time: 21126 seconds]
modified2020-07-07 17:30:41
created2007-07-27 17:23:01
id92755

Query times: 0.0003 seconds to select prime, 0.0002 seconds to seek comments.
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