Project Definition

Greenbank · 2006-01-11, 16:11

*** 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

fetofs · 2006-01-11, 16:42

Quote:

Originally Posted by Greenbank

*** Definition (by Dougy?)

The wording is Dougy's, I think.

Kosmaj · 2006-01-12, 23:24

You missed the most important information, namely that Octoproths were proposed by Robert Smith here.

robert44444uk · 2006-01-13, 17:09

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

henryzz · 2007-12-07, 18:41

does octo 6.0 follow the k<2^n limit

2006-01-11, 16:11	#1
Greenbank Jul 2005 2×193 Posts	Project Definition *** Definition (by Dougy) For natural numbers k,n, with k < 2^n, if the following are all primes: k2^n+1 k2^n-1 k2^(n+1)+1 k2^(n+1)-1 2^n+k 2^n-k 2^(n+1)+k 2^(n+1)-k then k2^n+1 is called an octoproth. It can be shown that if k2^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

2006-01-13, 17:09	#4
robert44444uk Jun 2003 Suva, Fiji 2³·3·5·17 Posts	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

Similar Threads
Thread	Thread Starter	Forum	Replies	Last Post
Definition of Sierpinski/Riesel number base b	sweety439	Conjectures 'R Us	33	2022-07-19 15:03
Definition of Merssene number	Unregistered	Information & Answers	5	2010-08-15 20:07
benchmarks over-clock definition?	lfm	PrimeNet	4	2009-11-15 00:43
Mersenne Numbers: Definition	R.D. Silverman	Math	47	2009-09-24 05:23
Mathematics definition	Damian	Lounge	1	2007-05-27 13:30

2006-01-12, 23:24	#3
Kosmaj Nov 2003 7046₈ Posts	You missed the most important information, namely that Octoproths were proposed by Robert Smith here.

2007-12-07, 18:41	#5
henryzz Just call me Henry "David" Sep 2007 Liverpool (GMT/BST) 37·163 Posts	does octo 6.0 follow the k<2^n limit