## Prime K-tuple patterns

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• 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
• ... 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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