Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

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 20, 2012 10:33 AM

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?
>
> --
>      The animated figures stand
>      And seem to breathe in stone, or
>      Move their marble feet.
>
>

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.
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.

Marcel Luttgens

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.