Riesel primes
For Riesel primes of the form k*2^n 1, I know K is an odd integer. What are the restrictions for the value of n?

I'm pretty sure it's only that n is such that 2^n>k (otherwise every number would be a Riesel number, and every prime a Riesel prime).

[QUOTE=MiniGeek;181486]I'm pretty sure it's only that n is such that 2^n>k (otherwise every number would be a Riesel number, and every prime a Riesel prime).[/QUOTE]
How would 2^n < k in of itself make a number riesel? I thought that any number of the form k*2^n 1 is a riesel number. 
[quote=Primeinator;181504]How would 2^n < k in of itself make a number riesel? I thought that any number of the form k*2^n 1 is a riesel number.[/quote]
I was mistaken about every number being represented by some k*2^n1. Every [I]odd[/I] number can be represented by k*2^n1 if 2^n can be less than k. Let's choose 15648132147819545 for example. 15648132147819545=k*2^n1 15648132147819546=k*2^n 15648132147819546 has only one factor of 2, so we set n to 1 2*7824066073909773=k*2 7824066073909773=k So 15648132147819545=7824066073909773*2^11 In case you're wondering, there is an identical requirement for Proth (k*2^n[B]+[/B]1) numbers. [url]http://en.wikipedia.org/wiki/Proth_number[/url] 
[QUOTE=MiniGeek;181542]I was mistaken about every number being represented by some k*2^n1. Every [I]odd[/I] number can be represented by k*2^n1 if 2^n can be less than k.
In case you're wondering, there is an identical requirement for Proth (k*2^n[B]+[/B]1) numbers. [url]http://en.wikipedia.org/wiki/Proth_number[/url][/QUOTE] Now that makes sense. And of course, with the exception of two, being odd is a necessity for any number x being a Riesel prime. However, you can still get an odd number by having n < k. A simple example: 3*2^2 1 = 11 = ! prime. 15*2^3  1 = 119 = ! prime Any number of k*2^n 1 will be odd, given k is odd. For n > k a prime can turn up. The first is k =3 and n = 6 which yields the following 3*2^6  1 = 191 = ! prime. Finally, n = k is also a possibility. 3*2^3 1 = 23 = ! prime. Apparently, all three scenarios are possible? 
if you search for a comprehensive collection of Riesel primes have a look at
[url]www.rieselprime.de[/url] BTW: n=k are called Woodall primes (see above link also) 
[QUOTE=kar_bon;181570]if you search for a comprehensive collection of Riesel primes have a look at
[url]www.rieselprime.de[/url] BTW: n=k are called Woodall primes (see above link also)[/QUOTE] From this site it appears that N is always bigger than k. However, even though the opposite can still produce a prime, is it considered a Riesel prime? 
[QUOTE=Primeinator;181573]From this site it appears that N is always bigger than k. However, even though the opposite can still produce a prime, is it considered a Riesel prime?[/QUOTE]
mhhh? have a look at the range for example 2000<k<4000 in the Data Section. only k=2001 got 24 primes with n<k!!! 
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. [URL="http://www.rieselprime.de"]www.rieselprime.de[/URL] lists primes when 2^n<k, even though these aren't technically Riesel numbers.
[quote=Primeinator;181562]Finally, n = k is also a possibility. 3*2^3 1 = 23 = ! prime.[/quote]This might interest you: n*2^n+1 is a [URL="http://mathworld.wolfram.com/CullenNumber.html"]Cullen Number[/URL]. (essentially a Proth number with k=n and no 2^n>k restriction; the Proth side equivalent of a Woodall number) [quote=Primeinator;181562]Apparently, all three scenarios are possible?[/quote]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. 
[QUOTE=Primeinator;181504]How would 2^n < k in of itself make a number riesel? I thought that any number of the form k*2^n 1 is a riesel number.[/QUOTE]
[b]Every[/b] single integer is of the form k*2^n  1. 
[quote=R.D. Silverman;181758][B]Every[/B] single integer is of the form k*2^n  1.[/quote]
Is this assuming k and n are integers? If so, I don't see how this could be. 
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