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Re: [PrimeNumbers] Re: Nash weights

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  • joe.mclean@it.glasgow.gov.uk
    Hello all. k = 138847 has a standard (negative) Nash weight of 29, which is very respectable for a reasonably small number. The lowest positive Nash weight I
    Message 1 of 6 , Mar 12, 2001
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      Hello all.

      k = 138847 has a standard (negative) Nash weight of 29, which is very
      respectable for a reasonably small number. The lowest positive Nash
      weight I found was 9 (yes, nine), so I'm sure that I could find
      something for the negative side in the low teens if I put my mind to
      it, though this would take some time with my current computers.

      However, if someone could write a very fast program for me, that would
      help. How about that Phil. Spookily, I was actually thinking about
      asking for this just last week. Great minds think alike. The logic is
      dead easy, honest.

      Joe.


      ______________________________ Reply Separator _________________________________
      Subject: [PrimeNumbers] Re: Nash weights
      Author: d.broadhurst@... at Internet
      Date: 12/03/01 01:38


      Jack Brennen wrote:

      > I have done some extensive calculations looking for high
      > Proth weights for both k*2^n+1 and k*2^n-1

      I like low weights, too.

      They have been studied for k*2^n+1.
      But in the Riesel case, k*2^n-1,
      I do not know of any lower non-zero
      weight than that for k=138847.

      138847*2^n-1 is prime for n=33 and for no other n<380,000.

      Is there any lower non-zero Nash weight with k<10^6,
      for k*2^n +/- 1 ?

      David



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    • Phil Carmody
      ... I find the measurements to be bizarre, in my mind I want a fractional value, and all these integers are out of range, so to speak. I guess that they re
      Message 2 of 6 , Mar 12, 2001
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        On Mon, 12 March 2001, joe.mclean@... wrote:
        > k = 138847 has a standard (negative) Nash weight of 29, which is very
        > respectable for a reasonably small number. The lowest positive Nash
        > weight I found was 9 (yes, nine), so I'm sure that I could find
        > something for the negative side in the low teens if I put my mind to
        > it, though this would take some time with my current computers.

        I find the measurements to be bizarre, in my mind I want a fractional value, and all these integers are out of range, so to speak. I guess that they're scaled, but why should they be?
        What is the "average" Nash weight? (not specifying which average, probably geometric). And what if this is normalised to 1?

        > However, if someone could write a very fast program for me, that would
        > help. How about that Phil. Spookily, I was actually thinking about
        > asking for this just last week. Great minds think alike. The logic is
        > dead easy, honest.

        Jack sent me a mail with a third modifier in it, independent of my first two modifiers. This was to do with (Aurefeulian?) factorisations of prime-power factors of k.

        I believe that if I have the definitive expression for a single number, then I can turn that into a (windowed) sieve technique. Who knows, I may even be able to write some "very fast code" for it. It appears to be a O(sqrt(N)) space, O(N) time algorithm, where N is the number itself, not the number of digits.

        Code like this must already have been written. I'm sure it;s easier for me to tweak than it is to start from scratch?

        Phil

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