20130815, 08:04  #12 
Jun 2003
1582_{10} Posts 
I think you got the point. Since no one is planning on testing the k beyond 10000 we can just test the low weight subsequences.
Generally the k that survive up to base=2^5760 are extremely high weight sequences to start with and hence it might be faster just to test them. What I don't know is, if these subsequences will produces primes as frequently as the other previous low weight sequences have. Last fiddled with by Citrix on 20130815 at 08:14 
20130815, 09:06  #13  
Feb 2003
2^{2}·3^{2}·53 Posts 
Quote:
On the other hand, one could imagine that some of the subsequences are fully covered (and therefore eliminated) by some larger (yet unknown) covering set(s)  making them "Riesel" candidates. The chances for this might be actually larger (due to the much larger base) than for the ordinary k. But I may be wrong with this assumption... 

20130815, 09:27  #14 
Jun 2003
2×7×113 Posts 
One goal would be to bring all the 818 k's with total nash weight of about 200 to n=2 million to see if any primes can be found.
Last fiddled with by Citrix on 20130815 at 09:28 
20130815, 09:30  #15  
Jun 2003
2·7·113 Posts 
Quote:
Does this mean that all subsequences will eventually produce a prime? 

20130815, 09:50  #16  
Feb 2003
2^{2}·3^{2}·53 Posts 
Quote:
IIRC, Joe McLean gave some examples on his pages: http://irvinemclean.com/maths/robintro.htm 

20130815, 09:58  #17  
Jun 2003
62E_{16} Posts 
Quote:
It is "almost impossible" to restrict the k to less than 2^18 and use numbers of 40 digits etc (large factors of 2^57601) to form the covering set. The odds of this happening would be in 1 in 10^30 for a 40 digit factor. 

20130815, 11:09  #18 
Feb 2003
2^{2}×3^{2}×53 Posts 
Well, the point here is that by switching to base 2^5760 you also introduce the "2^i" multipliers to your k, e.g. the transformation k > k*2^i (i=0...5759). Therefore most of your k's are actually much larger than just 2^18.
This, in turn, also gives rise to much larger (yet unknown) covering sets  the components of the set are no longer restricted to factors of 2^57601. Last fiddled with by Thomas11 on 20130815 at 11:12 
20130815, 15:41  #19  
Jun 2003
62E_{16} Posts 
Quote:
I estimate around 40,000. So the chance of there existing a larger covering set is very low. 

20130815, 18:27  #20  
Jun 2003
1582_{10} Posts 
Quote:
Quote:
Thomas11, I agree with what you are saying... but the odds of there existing a larger covering set for these k seems very small and hence unlikely. It is like asking for 2^p1 being prime for 2 consecutive primes (p> 1 million). It is possible they exist, but unlikely. 

20130815, 18:39  #21  
Feb 2003
3564_{8} Posts 
Quote:
What I mean is that there might be congruences for larger primes not being members of your original covering set (2^57601), or combinations of them (so called "virtual primes") which have just the matching orders to eliminate some (or even just a few) of your remaining sequences. Since they are already "fanned out" to 5760 bits, in my opinion, the chances are higher for such matching congruences. Anyway, one can just start the search on a bunch of your Ks and see what comes out. 

20130815, 19:34  #22  
Jun 2003
62E_{16} Posts 
Quote:


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