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Topic: A finite set of all naturals
Replies: 5   Last Post: Aug 24, 2013 1:22 AM

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Posts: 23
From: belgium
Registered: 8/22/13
the truth about primes and triangular numbers !!
Posted: Aug 23, 2013 4:20 PM
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Tommy's conjecture


Let t(1)=1 , t(2)=3 and t(n) be the n'th triangular number.

Let all variables be integers >= 1.

Let ... mean that we do not care about that structure.

Use the OLD definition of primes that includes 1 as a prime then :

Between t(a)-1 and t(a+1)+1 always exists at least 1 prime.

Between t(a)-1 and t(a+3)+1 always exists at least 1 prime twin.

Between t(a)-1 and t(a+2k+1)+1 always exists at least 1 prime constellation of the form(p,...,p+2k).




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