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Re: Vindication of Goldbach's conjecture
Posted:
Jun 22, 2012 6:40 AM
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On 22 juin, 03:19, Gus Gassmann <horand.gassm...@googlemail.com>
wrote:
> On Jun 21, 7:29 pm, mluttgens <lutt...@gmail.com> wrote:
>
> > For N = 1000000, one gets 10804 Goldbach's pairs.
> > The relation between log N and log n is log n = 0.727*log N -0.436
>
> Note that this is not an equation, as it is not satisfied for N = 4.
The linear relation has been calculated from N = 50 to N = 1000000.
Using it, one gets n = 8433 when N = 1000000, which is less than the
exact value 10804.
With the help of a graph, one could infer that another relationship,
probably exponential, would be more appropriate. This would of course
still clearer vindicate Goldbach's conjecture.
Marcel Luttgens
> It is at best an estimate, and there is error. This error may very
> well turn out to be bounded in such a way that n can never be zero,
> but you have not shown this. I will be generous and assume that to you
> "vindication" means something different than "proof". Note, however,
> that there are quite a few partial results already, based on a
> probabilistic analysis, see, e.g., the wikipedia article (http://
> en.wikipedia.org/wiki/Goldbach%27s_conjecture), along with some very
> nice pictures. None of this constitutes mathematical proof, however.
>
>
>
> > For N = 60,119,912, log n = 5.219 and the number of pairs is 165577
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