Remember that the restriction is 2^n>k, not n>k, so e.g. n=4 k=15 is allowed (2^4=16, 16>15) 15*2^41=239 which is prime.
www.rieselprime.de lists primes when 2^n<k, even though these aren't technically Riesel numbers.
Quote:
Originally Posted by Primeinator
Finally, n = k is also a possibility. 3*2^3 1 = 23 = ! prime.

This might interest you: n*2^n+1 is a
Cullen Number. (essentially a Proth number with k=n and no 2^n>k restriction; the Proth side equivalent of a Woodall number)
Quote:
Originally Posted by Primeinator
Apparently, all three scenarios are possible?

Apparently.
So...
When k*2^n+1 is prime, k*2^n+1 is called a Proth prime
When k*2^n1 is prime, k*2^n1 is called a Riesel prime
When k*2^n+1 is composite for every n with this specific k, k is called a Sierpinski number
When k*2^n1 is composite for every n with this specific k, k is called a Riesel number
When k*2^n+1 with odd k, positive integer n, and 2^n>k, k*2^n+1 is called a Proth number
When k*2^n1 with odd k, positive integer n, and 2^n>k, k*2^n1 is called ...what? (we're referring to it as Riesel number here, but that's technically incorrect since that refers to the equiv. of a Sierpinski number)
or in text: "Riesel number" technically refers to a k such that all k*2^n1 are composite, and "Riesel prime" refers to primes of the form k*2^n1, right? Is there any name for numbers of the form k*2^n1, analogous to "Proth number" for numbers of the form k*2^n+1? I know there is rarely confusion, at least in projects that aren't searching for Riesel numbers, but it is still an incorrect and vague reference.