9 · 23497442 + 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:9 · 23497442 + 1
Verification status (*):Proven
Official Comment:Generalized Fermat, divides GF(3497441,10)
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):L1780 : Ming, PSieve, Srsieve, PrimeGrid, LLR
Decimal Digits:1052836   (log10 is 1052835.90433754)
Rank (*):136 (digit rank is 1)
Entrance Rank (*):51
Currently on list? (*):short
Submitted:10/24/2012 19:11:32 CDT
Last modified:1/13/2014 16:20:03 CDT
Database id:109930
Status Flags:none
Score (*):46.791 (normalized score 21.3773)

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 (archivable *)
Prime on list: yes, rank 15
Subcategory: "Generalized Fermat"
(archival tag id 217581, tag last modified 2016-05-05 20:50:36)
Generalized Fermat Divisors (bases 3,5,6,10,12) (archivable *)
Prime on list: yes, rank 1, weight 48.9882333267294
Subcategory: "Divides GF(*,10)"
(archival tag id 217582, 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.

Chris Caldwell writes (11 Sep 2014): 
PrimeGrid notes that OpenGFN shows this prime divides each of GF(3497441,7), xGF(3497438,9,8), GF(3497441,10), xGF(3497439,11,3) and xGF(3497441,12,5).

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_id109930
person_id9
machineRedHat P4 P4
whattrial_divided
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 9 2 3497442 1 2>&1
[Elapsed time: 11.249 seconds]
modified2012-11-04 23:29:01
created2012-10-24 19:18:01
id149651

fieldvalue
prime_id109930
person_id9
machineDitto P4 P4
whatprime
notesCommand: /home/ditto/client/pfgw -t -q"9*2^3497442+1" 2>&1
PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5]
Primality testing 9*2^3497442+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%
9*2^3497442+1 is prime! (23500.7325s+0.0024s)
[Elapsed time: 6.53 hours]
modified2012-11-04 23:29:01
created2012-10-24 19:38:02
id149652

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