mersenneforum.org Naming k.2^n-1
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 2005-08-06, 08:40 #1 Dougy     Aug 2004 Melbourne, Australia 100110002 Posts Naming k.2^n-1 Numbers of the form k.2^n+1 with k<2^n are called Proth numbers. But is there a name for numbers of the form k.2^n-1 with k<2^n? And if there isn't, could someone suggest an appropriate name for them?
2005-08-06, 12:48   #2
TTn

438810 Posts

Quote:
 Numbers of the form k.2^n+1 with k<2^n are called Proth numbers. But is there a name for numbers of the form k.2^n-1 with k<2^n? And if there isn't, could someone suggest an appropriate name for them?
k.2^n-1 with k<2^n = Riesel
k.2^n+1 with k<2^n = Proth
k.2^n+-1 with k<2^n = Robinson (Generally)

 2005-08-06, 15:48 #3 Dougy     Aug 2004 Melbourne, Australia 2308 Posts I thought k.2^n-1 was called a Riesel number, however there is another definition that would cause some serious confusion. An odd number k such that k.2^n-1 is composite for all natural numbers n is called a Riesel number. MathWorld has this definition.
 2005-08-15, 17:20 #4 VBCurtis     "Curtis" Feb 2005 Riverside, CA 120518 Posts A Riesel number is a k-value that produces no Riesel Primes. A Riesel prime is a prime of the form mentioned. The semantics are confusing, but the definitions are not. -Curtis
2005-08-20, 17:35   #5

"Richard B. Woods"
Aug 2002
Wisconsin USA

22×3×641 Posts

Quote:
 Originally Posted by TTn k.2^n-1 with k<2^n = Riesel k.2^n+1 with k<2^n = Proth k.2^n+-1 with k<2^n = Robinson (Generally)
So the Riesel and Proth numbers are subsets of Robinson numbers?

Are they named after Raphael Mitchel Robinson ( http://www-groups.dcs.st-and.ac.uk/~...n_Raphael.html )?

Last fiddled with by cheesehead on 2005-08-20 at 17:36

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