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Old 2006-01-11, 16:11   #1
Greenbank
 
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Jul 2005

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Default Project Definition

*** Definition (by Dougy)

For natural numbers k,n, with k < 2^n, if the following are all primes:

k*2^n+1
k*2^n-1
k*2^(n+1)+1
k*2^(n+1)-1
2^n+k
2^n-k
2^(n+1)+k
2^(n+1)-k

then k*2^n+1 is called an octoproth.

It can be shown that if k*2^n+1 is an octoproth then k = 15 (mod 30) and if n != 1 (mod 3) then k = 105 mod 210

Last fiddled with by Greenbank on 2006-01-11 at 16:43
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Old 2006-01-11, 16:42   #2
fetofs
 
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Quote:
Originally Posted by Greenbank
*** Definition (by Dougy?)
The wording is Dougy's, I think.
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Old 2006-01-12, 23:24   #3
Kosmaj
 
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You missed the most important information, namely that Octoproths were proposed by Robert Smith here.
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Old 2006-01-13, 17:09   #4
robert44444uk
 
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Jun 2003
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Default The original source

If we are being pernickety, the concept was first mooted by me on Yahoo on Jan 26th 2004 when I called them "combo chains"

http://groups.yahoo.com/group/primen...6?viscount=100

Actually, I am sure others may well have thought about this before, and just never got it written down on the internet. But I certainly never got any response saying that the numbers had been researched previously.

Regards

Robert Smith
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Old 2007-12-07, 18:41   #5
henryzz
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does octo 6.0 follow the k<2^n limit
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