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Re: Vindication of Goldbach's conjecture
Posted:
Jun 22, 2012 8:21 AM
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In article <0556b041-cf5b-4b09-9b34-72473aebd922@n5g2000vbb.googlegroups.com>, mluttgens <luttgma@gmail.com> writes:
>On 17 juin, 20:17, quasi <qu...@null.set> wrote:
>> To prove Goldbach's Conjecture, you have to show, for the
>> general even n > 4, not a just a particular case, that a pair
>> of odd primes exists whose sum is n. That you haven't done.
>It was easy to show that the even number 26 is the sum of two primes:
>
>26 =3D 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.
Except when it doesn't:
450000 11028
455000 7526
460000 5840
which, by your reasoning, would show that Goldbach's conjecture is false.
>Perhaps could somebody finds a formula linking N and n.
>The given example shows that n cannot decrease from some value of N
>and eventually becomes zero.
>Thus, it vindicates Goldbach's conjecture.
The point isn't to show a general trend, but to show that it's *always*
the case. The general trend is what led Goldbach to make this conjecture,
and the reason that most mathematicians think that the conjecture is
probably true.
"Probably true" is easy; "proved" is hard.
--
Michael F. Stemper
#include <Standard_Disclaimer>
Life's too important to take seriously.
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