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

 Messages: [ Previous | Next ]
 mluttgens Posts: 80 Registered: 3/3/11
Re: Vindication of Goldbach's conjecture
Posted: Jun 21, 2012 6:29 PM

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
>      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.