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Re: Vindication of Goldbach's conjecture
Posted:
Jul 25, 2012 9:18 AM


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 = (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. > > 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 websites there ... > > In any case, Kevin Brown is listed in the Numericana Hall of Fame > along with other distinguished webauthors: > > <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



