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

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 David Bernier Posts: 3,892 Registered: 12/13/04
Re: Vindication of Goldbach's conjecture
Posted: Jul 24, 2012 2:09 PM

On 07/24/2012 10:52 AM, Ben Bacarisse wrote:
> 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
> 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: >>