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Re: Vindication of Goldbach's conjecture
Posted:
Jul 24, 2012 10:52 AM


mluttgens <luttgma@gmail.com> writes: <snip> > Thank you! You are of course right. > > But my aim was to show that a sum s? = a + b of two uneven numbers, at > least one of them not being a prime, could easily be transformed into > a sum of two primes, simply by adding and subtracting some even number > from its terms: > > The chosen example was: > > s? = 13 + 15 = (138) + (15+8) = 5+23 > = (132) + (15+2) = 11+17 > > It has been claimed that such transformation could sometimes not be > possible. > I am wondering about which terms a and b should be chosen to justify > that claim. > Till now, I did not find a clue in the litterature, but you have > perhaps a reference?
Your transformation is possible if GC it true and false otherwise. Every counterexample to GC (of which none are known, of course) would be an example of what you seek with s = 1 + (s1). Computers have checked GC up to about 10^18, but since almost everyone thinks GC is true, why would you go searching for a counterexample?
Every reference in the literature about GC is a reference that will help you in your quest, because your statement about transforming nonprime sums into prime sums is exactly the same as GC.
 Ben.



