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Old 2005-08-06, 08:40   #1
Dougy
 
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Post 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?
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Old 2005-08-06, 12:48   #2
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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)
 
Old 2005-08-06, 15:48   #3
Dougy
 
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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.
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Old 2005-08-15, 17:20   #4
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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
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Old 2005-08-20, 17:35   #5
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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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