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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 14, 2012 5:28 AM

On 10 juin, 00:20, rich...@cogsci.ed.ac.uk (Richard Tobin) wrote:
>
> mluttgens  <lutt...@gmail.com> wrote:

> >[deleted]
>
> You refuse to address the question; I conclude you are a troll.
>
> -- Richard
>
>

My response is contained in the following new version:

Vindication of Goldbach's conjecture
______________________________

According to the conjecture, every even integer greater than 4 can be
expressed as the sum of two primes.

Let's consider two identical infinite series S and S' of uneven
numbers, where S and S' = 3, 5, 7, 9, 11, 13, etc...
In other words, S(n) = S'(n) = 2n +1, with n beginning at 1.
Let?s note that S and S? contain only natural numbers.

The fact that some uneven numbers contained in the series S and S' can
be
the result of mathematical operations, for instance exponentiation, is
thus irrelevant.

By adding successively each number of S to all the numbers of S', one
gets a series P of even numbers.

Example:
_______

n S S'
_ _ _

1 3 3
2 5 5
3 7 7
4 9 9
5 11 11
6 13 13
7 15 15
8 17 17
9 19 19
10 21 21
11 23 23

By adding, one gets the following even numbers of series P:

From S = 3: 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26
From S = 5: 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28
From S = 7: 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30
From S = 9: 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32
From S = 11: 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34
From S = 13: 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36
From S = 15: 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38
From S = 17: 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40
From S = 19: 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42
From S = 21: 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44
From S = 23: 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46

Thus, series P contains all the even numbers from 6 to 46.

In P, the number 26 = 3+23, 5+21, 7+19, 9+17, 11+15, 13+13, 15+11,
17+9, 19+7, 21+5 and 23+3, all the terms coming from the successive
uneven numbers of S and S' from 3 to 23, where 23 = 26 - 3.
As S and S' contain all the prime numbers inferior or equal to 26-3 ,
the even number 26 is necessarily the sum of two primes.
Let?s note that it is not necessary to indentify those primes. Knowing
that they exist in S and S? is enough..
This applies mutatis mutandi to any even integer

Conclusion:

Every even integer greater than 4 can be expressed as the sum of two
primes.
In other words, the above procedure vindicates Goldbach's conjecture.

Marcel Luttgens

(June 11, 2012)

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.