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-   -   How to calculate Nash/robinson weight? (https://www.mersenneforum.org/showthread.php?t=11844)

 cipher 2009-05-08 03:15

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

 cipher 2009-05-08 03:17

 vaughan 2009-05-08 11:05

Huh - what the ... is that?

 kar_bon 2009-05-08 11:18

[QUOTE=vaughan;172845]Huh - what the ... is that?[/QUOTE]

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 n-values of a sieve for this k for n=100001-110000 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

 vaughan 2009-05-08 21:20

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?

 kar_bon 2009-05-08 21:42

as i explained, to find a prime you got a better chance by testing a high nash k-value but on the other hand you have to test many more n-values.

have a look a the NPLB Drive #10 page on [url]www.rieselprime.de[/url]

every 1000n-range contains about 11000 candidates to test (by 300 k-values overall).

Drive #9B shows for only [b]one[/b] k-value different counts for candidates (between about 1000 and 130000) depending on the nash-weight.

although the n-ranges are different, you can see on both drives there exist ranges with more or less primes.

so the idea to test a wide k-range is best to find primes and as a side-effect you test all!

 gd_barnes 2009-05-09 15:35

[quote=vaughan;172890]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?[/quote]

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

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