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Topic: Vindication of Goldbach's conjecture
Replies: 74   Last Post: Aug 9, 2012 6:50 PM

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 Michael Stemper Posts: 671 Registered: 6/26/08
Re: Vindication of Goldbach's conjecture
Posted: Jun 22, 2012 8:21 AM

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.

Date Subject Author
6/6/12 mluttgens
6/6/12 Brian Q. Hutchings
6/6/12 GEIvey
6/7/12 Richard Tobin
6/8/12 mluttgens
6/8/12 Count Dracula
6/9/12 mluttgens
6/9/12 Brian Q. Hutchings
6/9/12 mluttgens
6/25/12 GEIvey
6/9/12 Richard Tobin
6/9/12 mluttgens
6/9/12 Richard Tobin
6/9/12 Brian Q. Hutchings
6/9/12 Brian Q. Hutchings
6/14/12 mluttgens
6/16/12 mluttgens
6/16/12 Frederick Williams
6/20/12 mluttgens
6/20/12 Rick Decker
6/21/12 mluttgens
6/21/12 Frederick Williams
6/21/12 mluttgens
6/22/12 mluttgens
6/22/12 mluttgens
6/22/12 Brian Q. Hutchings
6/25/12 Michael Stemper
6/26/12 mluttgens
6/26/12 Frederick Williams
6/28/12 Michael Stemper
7/19/12 mluttgens
7/19/12 Timothy Murphy
7/19/12 mluttgens
7/19/12 Gus Gassmann
7/20/12 mluttgens
8/1/12 Tim Little
8/4/12 mluttgens
8/4/12 Frederick Williams
8/6/12 mluttgens
8/6/12 gus gassmann
8/6/12 Brian Q. Hutchings
8/9/12 Pubkeybreaker
7/19/12 J. Antonio Perez M.
7/20/12 mluttgens
6/25/12 Michael Stemper
6/25/12 Thomas Nordhaus
6/17/12 mluttgens
6/17/12 quasi
6/18/12 Count Dracula
6/18/12 quasi
6/19/12 Count Dracula
6/19/12 quasi
6/20/12 mluttgens
6/22/12 Michael Stemper
6/22/12 mluttgens
6/22/12 Robin Chapman
6/22/12 Michael Stemper
6/23/12 mluttgens
6/22/12 Richard Tobin
6/22/12 Richard Tobin
6/25/12 Richard Tobin
6/25/12 Michael Stemper
6/14/12 Count Dracula
6/21/12 Luis A. Rodriguez
6/21/12 Brian Q. Hutchings
6/21/12 mluttgens
6/25/12 GEIvey
6/20/12 J. Antonio Perez M.