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.

This prime's information:

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 (*):3776 (digit rank is 1)
Entrance Rank (*):57
Currently on list? (*):short
Submitted:6/22/2011 12:34:23 UTC
Last modified:3/11/2023 15:54:10 UTC
Database id:100563
Status Flags:none
Score (*):45.8136 (normalized score 2.1931)

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 11, weight 48.010920999694
Subcategory: "Divides GF(*,6)"
(archival tag id 214434, tag last modified 2023-03-31 01:37:05)
Generalized Fermat Divisors (bases 3,5,6,10,12) (archivable *)
Prime on list: yes, rank 15, weight 48.010920999694
Subcategory: "Divides GF(*,3)"
(archival tag id 214433, tag last modified 2024-03-22 08:37:11)
Fermat Divisors (archivable *)
Prime on list: yes, rank 8, weight 48.010920999694
Subcategory: "Divides Fermat"
(archival tag id 214432, tag last modified 2023-07-18 02:37:34)
Generalized Fermat Divisors (bases 3,5,6,10,12) (archivable *)
Prime on list: yes, rank 14, weight 48.010920999694
Subcategory: "Divides GF(*,12)"
(archival tag id 214435, tag last modified 2024-07-09 23:37:24)

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 (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)

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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.
machineDitto P4 P4
notesCommand: /home/ditto/client/TrialDiv/TrialDiv -q 9 2 2543551 1 2>&1 [Elapsed time: 11.163 seconds]
modified2020-07-07 22:30:31
created2011-06-22 12:35:01

machineDitto P4 P4
notesCommand: /home/ditto/client/pfgw -t -q"9*2^2543551+1" 2>&1 PFGW Version [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 22:30:31
created2011-06-22 12:38:01

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