Comments on: Today I learned http://hardwick.fi/blog/?p=1527 Sam Hardwick's web journal Wed, 01 Sep 2010 23:54:33 +0300 http://wordpress.org/?v=2.8.3 hourly 1 By: sam http://hardwick.fi/blog/?p=1527&cpage=1#comment-252 sam Tue, 06 Jul 2010 18:23:26 +0000 http://hardwick.fi/blog/?p=1527#comment-252 I can't, but it's based on 1) the representability of diophantine systems as polynomials 2) the formulation of primes as such a system (eg. <a href="http://mathdl.maa.org/mathDL/?pa=content&sa=viewDocument&nodeId=2967&pf=1" rel="nofollow">here</a>) If you inspect the polynomial closely, you notice that it has the form (k+2) * (1 - P(a,b,c...)^2 - P'(a,b,c...)^2 ...), so it will be positive only when all the polynomials P are zero. They essentially select the prime values of k+2. More <a href="http://en.wikipedia.org/wiki/Formula_for_primes#Formula_based_on_a_system_of_Diophantine_equations" rel="nofollow">on Wikipedia</a>. I can’t, but it’s based on

1) the representability of diophantine systems as polynomials
2) the formulation of primes as such a system (eg. here)

If you inspect the polynomial closely, you notice that it has the form

(k+2) * (1 – P(a,b,c…)^2 – P’(a,b,c…)^2 …), so it will be positive only when all the polynomials P are zero. They essentially select the prime values of k+2. More on Wikipedia.

]]> By: Vadim Kulikov http://hardwick.fi/blog/?p=1527&cpage=1#comment-250 Vadim Kulikov Tue, 06 Jul 2010 17:47:45 +0000 http://hardwick.fi/blog/?p=1527#comment-250 And the eighth power is the largest I can see? Wow, can you prove it? A lot of variables though.. And the eighth power is the largest I can see? Wow, can you prove it? A lot of variables though..

]]> By: sam http://hardwick.fi/blog/?p=1527&cpage=1#comment-234 sam Tue, 08 Jun 2010 19:33:20 +0000 http://hardwick.fi/blog/?p=1527#comment-234 Heh. The Green Parrot even sounds like my kind of place, judging from what Bess told me about it. Hope you're having a great time! Heh. The Green Parrot even sounds like my kind of place, judging from what Bess told me about it. Hope you’re having a great time!

]]> By: Neil Hardwick http://hardwick.fi/blog/?p=1527&cpage=1#comment-233 Neil Hardwick Tue, 08 Jun 2010 18:36:38 +0000 http://hardwick.fi/blog/?p=1527#comment-233 Funny thing - Bess and I were just talking about this very same thing here in the Green Parrot in Key West! Funny thing – Bess and I were just talking about this very same thing here in the Green Parrot in Key West!

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