# 9 · 22543551 + 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 · 22543551 + 1 Proven Divides Fermat F(2543548), GF(2543549,3), GF(2543549,6), GF(2543549,12) This prime has 1 user comment below. L1204 : Brown1, PSieve, Srsieve, PrimeGrid, LLR 765687   (log10 is 765686.10074363) 1353 (digit rank is 1) 57 short 6/22/2011 07:34:23 CDT 7/14/2012 13:50:36 CDT 100563 none 45.8136 (normalized score 4.813)

#### 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 5, weight 48.0109209996937
Subcategory: "Divides GF(*,6)"
Generalized Fermat Divisors (bases 3,5,6,10,12) (archivable *)
Prime on list: yes, rank 11, weight 48.0109209996937
Subcategory: "Divides GF(*,3)"
Fermat Divisors (archivable *)
Prime on list: yes, rank 6, weight 48.0109209996937
Subcategory: "Divides Fermat"
Generalized Fermat Divisors (bases 3,5,6,10,12) (archivable *)
Prime on list: yes, rank 6, weight 48.0109209996937
Subcategory: "Divides GF(*,12)"

PrimeGrid writes (11 Sep 2014):  (report abuse)
 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.
fieldvalue
prime_id100563
person_id9
machineDitto P4 P4
whattrial_divided
notesCommand: /home/ditto/client/TrialDiv/TrialDiv -q 9 2 2543551 1 2>&1 [Elapsed time: 11.163 seconds]
modified2020-07-07 17:30:31
created2011-06-22 07:35:01
id130690

fieldvalue
prime_id100563
person_id9
machineDitto P4 P4
whatprime
notesCommand: /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]
modified2020-07-07 17:30:31
created2011-06-22 07:38:01
id130691

Query times: 0.0017 seconds to select prime, 0.0007 seconds to seek comments.