20090718, 02:52  #1 
"Kyle"
Feb 2005
Somewhere near M52..
3·5·61 Posts 
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?

20090718, 02:54  #2 
Account Deleted
"Tim Sorbera"
Aug 2006
San Antonio, TX USA
17·251 Posts 
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).
Last fiddled with by MiniGeek on 20090718 at 02:55 
20090718, 05:54  #3 
"Kyle"
Feb 2005
Somewhere near M52..
3·5·61 Posts 

20090718, 12:34  #4  
Account Deleted
"Tim Sorbera"
Aug 2006
San Antonio, TX USA
17·251 Posts 
Quote:
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+1) numbers. http://en.wikipedia.org/wiki/Proth_number 

20090718, 15:23  #5  
"Kyle"
Feb 2005
Somewhere near M52..
3·5·61 Posts 
Quote:
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? 

20090718, 15:50  #6 
Mar 2006
Germany
2×11×131 Posts 
if you search for a comprehensive collection of Riesel primes have a look at
www.rieselprime.de BTW: n=k are called Woodall primes (see above link also) Last fiddled with by kar_bon on 20090718 at 15:51 
20090718, 16:05  #7  
"Kyle"
Feb 2005
Somewhere near M52..
3·5·61 Posts 
Quote:


20090718, 16:19  #8  
Mar 2006
Germany
B42_{16} Posts 
Quote:
have a look at the range for example 2000<k<4000 in the Data Section. only k=2001 got 24 primes with n<k!!! 

20090718, 16:49  #9  
Account Deleted
"Tim Sorbera"
Aug 2006
San Antonio, TX USA
17×251 Posts 
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:
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. 

20090719, 19:14  #10 
Nov 2003
2^{2}·5·373 Posts 

20090719, 23:14  #11 
Account Deleted
"Tim Sorbera"
Aug 2006
San Antonio, TX USA
17×251 Posts 

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