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Re: Vindication of Goldbach's conjecture
Posted:
Jun 21, 2012 6:29 PM
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On 21 juin, 15:08, Frederick Williams <freddywilli...@btinternet.com>
wrote:
> mluttgens wrote:
>
> > On 16 juin, 19:00, Frederick Williams <freddywilli...@btinternet.com>
> > wrote:
> > > mluttgens wrote:
>
> > > > Bigger is the number, and more primes it contains.
> > > > Hence, the number of possible sums of two primes corresponding to a
> > > > number
> > > > is proportional to the magnitude of the number.
>
> > > That's a big claim. Can you prove it?
>
> > It was easy to show that the even number 26 is the sum of two primes:
>
> > 26 = 3+23, 7+19, 13+13, 19+7 and 23+3.
>
> > Let's call those sums Goldbach's sums.
> > The number 26 has thus 5 Goldbach's sums. Hence, the number 26
> > vindicates Goldbach's conjecture.
>
> > In order to falsify the conjecture, one should need to show that some
> > even number can't be the sum of two primes.
>
> > Hereafter are the numbers n of Goldbach's sums for increasing even
> > numbers N:
>
> > N n
> > _ _
>
> > 50 8
> > 100 12
> > 500 26
> > 1000 56
> > 5000 152
> > 10000 254
> > 50000 900
> > 100000 1628
>
> > Clearly, when N increases, the number of Goldbach's sums also
> > increases.
>
> There's no 'clearly' about it. You've gone up to 100,000 (have you even
> done that, or just looked at some numbers up to 100,000?); what about N
>
> > 100,000?
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
For N = 60,119,912, log n = 5.219 and the number of pairs is 165577
Marcel Luttgens
>
> --
> The animated figures stand
> Adorning every public street
> And seem to breathe in stone, or
> Move their marble feet.
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