9 · 29431 + 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:9 · 29431 + 1
Verification status (*):Proven
Official Comment (*):Divides Fermat F(9428); GF(9429,6), GF(9429,12) [D]; GF(9429,3) [BR]
Proof-code(s): (*):K : Keller
Decimal Digits:2840   (log10 is 2839.9681316165)
Rank (*):93012 (digit rank is 1)
Entrance Rank (*):25
Currently on list? (*):no
Last modified:8/30/2007 13:38:59 CDT
Database id:29962
Status Flags:none
Score (*):28.5298 (normalized score 0)

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: no, rank 80, weight 30.72707804684
Subcategory: "Divides GF(*,12)"
(archival tag id 185826, tag last modified 2022-04-12 17:37:10)
Generalized Fermat Divisors (bases 3,5,6,10,12) (archivable *)
Prime on list: no, rank 72, weight 30.72707804684
Subcategory: "Divides GF(*,6)"
(archival tag id 185825, tag last modified 2022-05-12 21:37:21)
Fermat Divisors (archivable *)
Prime on list: no, rank 70, weight 30.72707804684
Subcategory: "Divides Fermat"
(archival tag id 185824, tag last modified 2021-01-16 15:20:20)
Generalized Fermat Divisors (bases 3,5,6,10,12) (archivable *)
Prime on list: no, rank 86, weight 30.72707804684
Subcategory: "Divides GF(*,3)"
(archival tag id 185827, tag last modified 2021-02-26 11:20:20)

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.
machineLinux PII 200
notesPFGW Version 1.1 for Pentium and compatibles Running N-1 test using base 5 Primality testing 9*2^9431+1 [N-1, Brillhart-Lehmer-Selfridge] Calling Brillhart-Lehmer-Selfridge with factored part 99.97% 9*2^9431+1 is prime! (8.540000 seconds)
modified2003-03-25 11:26:38
created2002-12-06 16:12:44

Query times: 0.0002 seconds to select prime, 0.0002 seconds to seek comments.
Printed from the PrimePages <primes.utm.edu> © Chris Caldwell.