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Old 2011-07-26, 23:49   #1
LiquidNitrogen
 
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Default Nash Weights vs. Sievability

I am wondering if there is a relationship governing how well a candidate Riesel prime is sieved vs. its Nash weight.

It seems that low Nash weights, which generate fewer primes, also seive very well. Very high Nash weights, which generate many more primes per exponent range, don't seem to respond well to sieving.

Is there a reason for this, or is this a misnomer?
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Old 2011-07-27, 02:48   #2
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For a more exact answer, provide a more exact definition of 'sievability' and related terms.
As far as I know, and I know that I, and probably others, have done some testing to determine how many primes you end up with with low vs high weight bases/k's: there is no significant difference in the probability of any single low-weight k candidate being prime and a similar candidate for a high-weight k. E.g. if a certain k is 5 times the weight of a low weight k, and k is insignificant compared to b^n, after sieving a certain n range for both to the same depth, you'll expect almost exactly 5 times more primes with the high weight k than the low weight one, because there will be almost exactly 5 times more candidates to test.
But now for the focus of your question: sieving. I wouldn't be surprised if the optimal sieve bounds for 1, 2, and 3+ k-searches look a bit different depending on the weights of the k's, due to how sieving works. But my slightly-educated guess says that the high-weight ones are better off than the low-weight ones.
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Old 2011-07-29, 23:14   #3
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Quote:
Originally Posted by Mini-Geek View Post
For a more exact answer, provide a more exact definition of 'sievability' and related terms.
I looked at some constants with Nash weights < 2500. After the "initial sieving" in NewPGen, where it first displays the results after a period of noise free operation, some of them had already eliminated 93% of the candidates. After longer sieving, it would creep up to 95% before requiring more time to just LLR the rest.

Some constants with Nash weights > 6000 would hardly pass 80% after the same period of time, and they would reach 85% after a full 24 hours of sieving.

My guess from this limited experiment would be that a high Nash weight generates more candidate primes as well as more "real" primes in a given range of exponents.

If this is true, the question remains, does it take less time to find "X" primes over an unbounded range with a lower Nash weight and better sieving, or a higher Nash weight with more candidates to examine?

Last fiddled with by LiquidNitrogen on 2011-07-29 at 23:16
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Old 2011-07-29, 23:25   #4
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Use sr<x>sieve instead of newpgen. It blows newpgen away for k*b^n+/-1 sequences.
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Old 2011-07-30, 09:15   #5
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Quote:
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Use sr<x>sieve instead of newpgen. It blows newpgen away for k*b^n+/-1 sequences.
Or FermFact 2.0 for "rectangular search" (multiple n and k for k*2^n+1).

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Old 2011-07-31, 20:22   #6
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Quote:
Originally Posted by ET_ View Post
Or FermFact 2.0 for "rectangular search" (multiple n and k for k*2^n+1).

Luigi
I can only find links to FermFact 0.9 can you show me where to download it?
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Old 2011-08-01, 10:58   #7
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Quote:
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I can only find links to FermFact 0.9 can you show me where to download it?
I'm in updating my site, the link doesn't appear yet.

http://www.fermatsearch.org/FermFact-2.0.zip

Luigi
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Old 2011-08-03, 03:06   #8
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Quote:
Originally Posted by ET_ View Post
I'm in updating my site, the link doesn't appear yet.

http://www.fermatsearch.org/FermFact-2.0.zip

Luigi
Many thanks!
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