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