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 · 22543551 + 1 Verification status (*): Proven Official Comment: Divides Fermat F(2543548), GF(2543549,3), GF(2543549,6), GF(2543549,12) Unofficial Comments: This prime has 1 user comment below. Proof-code(s): (*): L1204 : Brown1, PSieve, Srsieve, PrimeGrid, LLR Decimal Digits: 765687   (log10 is 765686.10074363) Rank (*): 126 (digit rank is 1) Entrance Rank (*): 57 Currently on list? (*): short Submitted: 6/22/2011 07:34:23 CDT Last modified: 7/14/2012 13:50:36 CDT Database id: 100563 Status Flags: none Score (*): 45.8136 (normalized score 20.0216)

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 3, weight 48.0109209996937
Subcategory: "Divides GF(*,6)"
(archival tag id 214434, tag last modified 2013-05-20 20:50:27)

Generalized Fermat Divisors (bases 3,5,6,10,12) (archivable *)

Prime on list: yes, rank 5, weight 48.0109209996937
Subcategory: "Divides GF(*,3)"
(archival tag id 214433, tag last modified 2013-04-28 21:50:30)

Fermat Divisors (archivable *)

Prime on list: yes, rank 2, weight 48.0109209996937
Subcategory: "Divides Fermat"
(archival tag id 214432, tag last modified 2013-05-14 17:50:05)

Generalized Fermat Divisors (bases 3,5,6,10,12) (archivable *)

Prime on list: yes, rank 3, weight 48.0109209996937
Subcategory: "Divides GF(*,12)"
(archival tag id 214435, tag last modified 2013-03-05 15:20:04)

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 (23 Jun 2011): 

9*2^2543551+1 Divides Fermat F(2543548) 9*2^2543551+1 Divides GF(2543549,3) 9*2^2543551+1 Divides xGF(2543549,3,2) 9*2^2543551+1 Divides xGF(2543549,4,3) 9*2^2543551+1 Divides GF(2543549,6) 9*2^2543551+1 Divides xGF(2543549,8,3) 9*2^2543551+1 Divides xGF(2543542,9,2) 9*2^2543551+1 Divides xGF(2543547,9,8) 9*2^2543551+1 Divides GF(2543550,11) 9*2^2543551+1 Divides xGF(2543550,11,2) 9*2^2543551+1 Divides xGF(2543550,11,3) 9*2^2543551+1 Divides xGF(2543550,11,4) 9*2^2543551+1 Divides xGF(2543550,11,6) 9*2^2543551+1 Divides xGF(2543550,11,8) 9*2^2543551+1 Divides xGF(2543550,11,9) 9*2^2543551+1 Divides GF(2543549,12) 9*2^2543551+1 Divides xGF(2543550,12,11) 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.

field value prime_id 100563 person_id 9 machine Ditto P4 P4 what trial_divided notes Command: /home/ditto/client/TrialDiv/TrialDiv -q 9 2 2543551 1 2>&1 [Elapsed time: 11.163 seconds] modified 2011-12-27 16:48:32 created 2011-06-22 07:35:01 id 130690

field value prime_id 100563 person_id 9 machine Ditto P4 P4 what prime notes Command: /home/ditto/client/pfgw -t -q"9*2^2543551+1" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing 9*2^2543551+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 5 Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 9*2^2543551+1 is prime! (13803.0144s+0.0017s) [Elapsed time: 3.83 hours] modified 2011-12-27 16:48:32 created 2011-06-22 07:38:01 id 130691