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

 Messages: [ Previous | Next ]
 Frederick Williams Posts: 2,164 Registered: 10/4/10
Re: Vindication of Goldbach's conjecture
Posted: Jun 21, 2012 9:08 AM

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?

--
The animated figures stand
Adorning every public street
And seem to breathe in stone, or
Move their marble feet.

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.