9 · 23497442 + 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:9 · 23497442 + 1
Verification status (*):Proven
Official Comment (*):Generalized Fermat, divides GF(3497441,10)
Unofficial Comments:This prime has 2 user comments below.
Proof-code(s): (*):L1780 : Ming, PSieve, Srsieve, PrimeGrid, LLR
Decimal Digits:1052836   (log10 is 1052835.9043375)
Rank (*):1178 (digit rank is 1)
Entrance Rank (*):51
Currently on list? (*):short
Submitted:10/25/2012 00:11:32 UTC
Last modified:3/11/2023 15:54:10 UTC
Database id:109930
Status Flags:none
Score (*):46.791 (normalized score 7.2566)

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: no, rank 447
Subcategory: "Generalized Fermat"
(archival tag id 217581, tag last modified 2023-09-24 13:37:27)
Generalized Fermat Divisors (bases 3,5,6,10,12) (archivable *)
Prime on list: yes, rank 5, weight 48.988233326729
Subcategory: "Divides GF(*,10)"
(archival tag id 217582, tag last modified 2023-07-02 21:37:20)

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):  (report abuse)
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).

PrimeGrid writes (27 Nov 2016):  (report abuse)
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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 9 2 3497442 1 2>&1 [Elapsed time: 11.249 seconds]
modified2020-07-07 22:30:23
created2012-10-25 00:18:01

machineDitto P4 P4
notesCommand: /home/ditto/client/pfgw -t -q"9*2^3497442+1" 2>&1 PFGW Version [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]
modified2020-07-07 22:30:23
created2012-10-25 00:38:02

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