20110726, 23:49  #1 
Jun 2011
Henlopen Acres, Delaware
7·19 Posts 
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? 
20110727, 02:48  #2 
Account Deleted
"Tim Sorbera"
Aug 2006
San Antonio, TX USA
17·251 Posts 
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 lowweight k candidate being prime and a similar candidate for a highweight 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+ ksearches look a bit different depending on the weights of the k's, due to how sieving works. But my slightlyeducated guess says that the highweight ones are better off than the lowweight ones. 
20110729, 23:14  #3  
Jun 2011
Henlopen Acres, Delaware
7·19 Posts 
Quote:
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 20110729 at 23:16 

20110729, 23:25  #4 
"Mark"
Apr 2003
Between here and the
3·2,081 Posts 
Use sr<x>sieve instead of newpgen. It blows newpgen away for k*b^n+/1 sequences.

20110730, 09:15  #5 
Banned
"Luigi"
Aug 2002
Team Italia
1001011000000_{2} Posts 

20110731, 20:22  #6 
Jun 2011
Henlopen Acres, Delaware
133_{10} Posts 

20110801, 10:58  #7  
Banned
"Luigi"
Aug 2002
Team Italia
2^{6}·3·5^{2} Posts 
Quote:
http://www.fermatsearch.org/FermFact2.0.zip Luigi 

20110803, 03:06  #8  
Jun 2011
Henlopen Acres, Delaware
205_{8} Posts 
Quote:


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