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2009-05-09, 15:35   #7
gd_barnes

May 2007
Kansas; USA

22×17×149 Posts

Quote:
 Originally Posted by vaughan 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?
No. There would be no benefit one way or another. It makes no difference on the amount of time it takes or the chance of finding a prime for each k/n pair searched if they are all sieved to the same depth. Sure, high-weight k's will have many more primes but that's because there are a lot more pairs to search because they have few small factors. On the other hand, low-weight k's have few pairs to search because they have many small factors. Therefore we search them all, regardless of weight, to fill in all the holes.

On a related topic, a Riesel number is a k-value 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 n-values 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 k-value like RieselSieve did and Seventeen-or-Bust does.

The math on much of this stuff is high-level high-school or low-level 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 2009-05-09 at 15:38