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Prime K-tuple patterns

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  • Tom
    Patterns page: http://www.opertech.com/primes/k-tuples.html Plot: http://www.opertech.com/primes/trophy.bmp Trophies (extremes)
    Message 1 of 2 , Sep 3, 2008
      Patterns page:
      http://www.opertech.com/primes/k-tuples.html

      Plot:
      http://www.opertech.com/primes/trophy.bmp

      Trophies (extremes)
      http://www.opertech.com/primes/trophycase.html

      Related:
      http://www.opertech.com/primes/modexample.html

      Modulii for 3159 (current upper boud):
      http://www.opertech.com/primes/w3159.html

      Text document of current maximum densities:
      http://www.opertech.com/primes/summary.txt

      For those interested the k-tuple pattern
      pages have been updated. This will be the
      last update for some time, as I am going to
      proceed with rewriting the exhaustive search
      program (this time without an upper limit)
      in an attempt to further reduce the range
      of the first contradiction to the HL
      conjecture pi(x+y)-pi(x)<=pi(y).

      Currently the bounds are 2077 < y <= 3159
      and prelim calculations say I should be
      able to achieve raising the lower bound
      to about 2300 using my home PC.

      Thomas J Engelsma
    • Phil Carmody
      ... Can you write this in a way such that the task can be distributed over multiple machines? If so, and the code s portable, then I can stick 2*2 GHz of G5
      Message 2 of 2 , Sep 4, 2008
        --- On Thu, 9/4/08, Tom <tom@...> wrote:
        > Patterns page:
        > http://www.opertech.com/primes/k-tuples.html

        > For those interested the k-tuple pattern
        > pages have been updated. This will be the
        > last update for some time, as I am going to
        > proceed with rewriting the exhaustive search
        > program (this time without an upper limit)
        > in an attempt to further reduce the range
        > of the first contradiction to the HL
        > conjecture pi(x+y)-pi(x)<=pi(y).
        >
        > Currently the bounds are 2077 < y <= 3159
        > and prelim calculations say I should be
        > able to achieve raising the lower bound
        > to about 2300 using my home PC.

        Can you write this in a way such that the task can be distributed over multiple machines? If so, and the code's portable, then I can stick 2*2 GHz of G5 processors (running either OSX or Linux) onto such a task. There might be others who would be willing to take small chunks too. What's the Big-Oh of the problem - how hard is pushing from 2300-2400 compared with pushing from 2200-2300?

        Phil
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