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Topic: Vindication of Goldbach's conjecture
Replies: 4   Last Post: Jul 25, 2012 9:18 AM

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Ben Bacarisse

Posts: 994
Registered: 7/4/07
Re: Vindication of Goldbach's conjecture
Posted: Jul 24, 2012 10:52 AM
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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 = (13-8) + (15+8) = 5+23
> = (13-2) + (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 counter-example to GC (of which none are known, of course) would be
an example of what you seek with s = 1 + (s-1). Computers have checked
GC up to about 10^18, but since almost everyone thinks GC is true, why
would you go searching for a counter-example?

Every reference in the literature about GC is a reference that will
help you in your quest, because your statement about transforming
non-prime sums into prime sums is exactly the same as GC.

--
Ben.



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