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

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 Rick Decker Posts: 1,354 Registered: 12/6/04
Re: Vindication of Goldbach's conjecture
Posted: Jun 20, 2012 11:35 AM

On 6/20/12 10:33 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?
>>
>> --
>> 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.

No. All you can say with certainty is that _for the cases you have
provided_, the number of Goldbach sums increases as N increases.
You haven't provided anything of substance besides your assertion.

> Perhaps could somebody finds a formula linking N and n.

Now _that_ would indeed be a useful result. The problem is that
nobody has come up with such a formula.

> The given example shows that n cannot decrease from some value of N
> and eventually becomes zero.

No it doesn't. It only provides a reason why you believe that GC is
true. Being as gentle as I can here, no one is interested in your
beliefs. Lots of mathematicians believe that GC is true, but they
recognize that belief without proof isn't mathematics.

> Thus, it vindicates Goldbach's conjecture.

Sorry to break it to you, but it doesn't, at least for any
definition of "vindicate" that I could find.

Regards,

Rick

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.