Date: Jul 25, 2012 9:18 AM
Author: mluttgens
Subject: Re: Vindication of Goldbach's conjecture

On 24 juil, 20:09, David Bernier <david...@videotron.ca> wrote:
> On 07/24/2012 10:52 AM, Ben Bacarisse wrote:
>
>
>
>
>

> > mluttgens<lutt...@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.

>
> Kevin Brown has a rather unique kind of presence on the Web.
> His math pages rarely mention the name of the author (himself).
> I read that there are no links going to other web-sites there ...
>
> In any case, Kevin Brown is listed in the Numericana Hall of Fame
> along with other distinguished web-authors:
>
> <http://www.numericana.com/fame/> .
>
> ---
>
> In his essay "Evidence for Goldbach", Brown tries to
> compensate the number of prime partitions of an even number
> 2n for/(according to) the residue class (modulo 3) of 2n, with
> a logical argument.  There's further compensation
> [justified probabilistically] for 2n (modulo p)
> for all larger odd primes p.
>
> The end result, quoting K.B.,
> << If we plot the log of
> this function divided by the log of n we find that the scatter is
> reduced almost entirely to a single line as shown below: >>
>
> Link to his essay below:
> <http://www.mathpages.com/home/kmath101.htm> .
>
> Dave
>
>


Thanks! This is an interesting approach.

Marcel Luttgens