20090508, 03:15  #1 
Feb 2007
211 Posts 
How to calculate Nash/robinson weight?
I had a program which was able to calculate Nash/robinson Weight for me.
I don't have the program any more? does any one have that program or know how i can calculate Nash/robinson weight for a particular "k". Also i have some confusion about the Definition on Nash & Robinson weight. so if you can clarify that also. thanks cipher 
20090508, 03:17  #2 
Feb 2007
211 Posts 

20090508, 11:05  #3 
Jan 2005
Sydney, Australia
5×67 Posts 
Huh  what the ... is that?

20090508, 11:18  #4 
Mar 2006
Germany
2^{8}·11 Posts 
the Nash weight is like an indicator how much prime n's for a special k there could be found.
it's the number of remaining nvalues of a sieve for this k for n=100001110000 and prime factors (sieve depth) upto p=512. so the higher the Nash weight the more candidates left and the more prime n you could expect. i always display this value on my RieselPrimeDatabase:  a low weight is smaller then 1000  a heigh weight is about 4000 and more 
20090508, 21:20  #5 
Jan 2005
Sydney, Australia
5×67 Posts 
Thank you for the explanation kar_bon. The longer I hang around on this forum the more I keep learning about all this Mathematics stuff.
So is it better for the NPLB project if we clean up the high Nash weight numbers (ranges) in preference to the low weight numbers? 
20090508, 21:42  #6 
Mar 2006
Germany
2^{8}·11 Posts 
as i explained, to find a prime you got a better chance by testing a high nash kvalue but on the other hand you have to test many more nvalues.
have a look a the NPLB Drive #10 page on www.rieselprime.de every 1000nrange contains about 11000 candidates to test (by 300 kvalues overall). Drive #9B shows for only one kvalue different counts for candidates (between about 1000 and 130000) depending on the nashweight. although the nranges are different, you can see on both drives there exist ranges with more or less primes. so the idea to test a wide krange is best to find primes and as a sideeffect you test all! 
20090509, 15:35  #7  
May 2007
Kansas; USA
2^{5}×317 Posts 
Quote:
On a related topic, a Riesel number is a kvalue with a Nash weight of ZERO! That means it has ZERO pairs remaining after sieving and hence never has a prime because all of the nvalues are eliminated by small factors. The lowest Riesel number for base 2 is k=509203. The RieselSieve project had set out to find a prime for all k's < 509203. Alas, when the project went down, there were still 64 k's remaining with no prime that SHOULD have a prime at some point. I believe all had been searched to n>=3M. The CRUS project, the sister project of NPLB, that I started about a month before it, searches for primes for all k's on different bases than base 2. It stops searching when it finds a prime for a specific kvalue like RieselSieve did and SeventeenorBust does. The math on much of this stuff is highlevel highschool or lowlevel college stuff. Most of it is not hard at all. If you "kind of" like some of the math related to this stuff, there are a few people who can give you all kinds of fun info. about it, even in laymen's terms. :) Gary Last fiddled with by gd_barnes on 20090509 at 15:38 

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