243 · 2495732 + 1
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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:243 · 2495732 + 1
Verification status (*):Proven
Official Comment:Divides Fermat F(495728), GF(495726,3), GF(495728,6), GF(495727,12)
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):L165 : Keiser, NewPGen, OpenPFGW, LLR
Decimal Digits:149233   (log10 is 149232.58741677)
Rank (*):32658 (digit rank is 1)
Entrance Rank (*):976
Currently on list? (*):short
Submitted:5/29/2007 14:02:13 CDT
Last modified:5/30/2007 09:30:31 CDT
Database id:80777
Status Flags:none
Score (*):40.7872 (normalized score 0.0462)

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 24, weight 46.2802618490471
Subcategory: "Divides GF(*,12)"
(archival tag id 187409, tag last modified 2016-03-15 13:57:15)
Generalized Fermat Divisors (bases 3,5,6,10,12) (archivable *)
Prime on list: no, rank 27, weight 46.2802618490471
Subcategory: "Divides GF(*,6)"
(archival tag id 187408, tag last modified 2016-03-15 13:57:15)
Generalized Fermat Divisors (bases 3,5,6,10,12) (archivable *)
Prime on list: no, rank 33, weight 46.2802618490471
Subcategory: "Divides GF(*,3)"
(archival tag id 187407, tag last modified 2016-03-15 13:57:15)
Fermat Divisors (archivable *)
Prime on list: yes, rank 19, weight 46.2802618490471
Subcategory: "Divides Fermat"
(archival tag id 187406, tag last modified 2016-03-15 13:57:14)

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.

Reto Keiser writes (11 Sep 2014): 
Divides F(495728), GF(495726,3), GF(495728,6), GF(495727,12), GF(495728,18), GF(495728,24), GF(495726,27), xGF(495728,3,2), xGF(495727,4,3), xGF(495728,8,3), xGF(495728,9,2), xGF(495728,9,8), xGF(495725,16,3), xGF(495728,27,2), xGF(495727,27,4), xGF(495728,8), xGF(495724,27,16)

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/pfgw -t -q"243*2^495732+1" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing 243*2^495732+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 7
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(65536,20) to FFT(65536,19)
Reduced from FFT(65536,19) to FFT(65536,18)
Reduced from FFT(65536,18) to FFT(65536,17)
Reduced from FFT(65536,17) to FFT(65536,16)
991488 bit request FFT size=(65536,16)
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%
243*2^495732+1 is prime! (1345.7600s+0.0000s)
[Elapsed time: 1352 seconds]
modified2007-05-30 21:58:14
created2007-05-29 14:04:36

machineRedHat P4 P4
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 243 2 495732 1 2>&1
[Elapsed time: 9.425 seconds]
modified2007-05-30 21:58:14
created2007-05-29 14:22:02

Query times: 0.0004 seconds to select prime, 0.0007 seconds to seek comments.