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

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 Luis A. Rodriguez Posts: 748 Registered: 12/13/04
Re: Vindication of Goldbach's conjecture
Posted: Jun 21, 2012 1:50 PM

El jueves, 14 de junio de 2012 10:24:12 UTC-4:30, Count Dracula escribió:
> On Jun 14, 5:28 am, mluttgens <lutt...@gmail.com> wrote:
> > 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..

>
> The argument you give here is fallacious. The sets S and S' also
> contain odd
> numbers that are not prime. This makes it necessary to identify the
> particular
> primes and it is not enough to know that primes exist in S and S'. In
> your
> example for 26, it is not possible to use the sums 5+21, 9+17, 11+15,
> 15+11,
> 17+9, 21+5 since each contains a composite integer. My earlier
> question to you was: what if there is an integer for which _all_ the
> sums
> are inadmissable, not just some as in the case of 26? Nothing in your
> argument rules out this possibility.
>
> If a counterexample exists it will have to be larger that 10^17
> because
> computer verifications have been performed up to about that value. A
> correct
> proof is highly likely to require some highly technical innovations.
>
> Count Dracula

The true difficult with Goldbach's Conjecture is this:
Given a even number 2k to warrant that the pairing of the
two arithmetic progressions 2n + 1 and 2k - (2n+1) will produce
nor less than one coincidence of two primes.
Example.- Given the even number 98. The two progressions are:

3, 5, 7, 9, 11, 13, 15, 17,.........95
95, 93, 91, 89, 87, 85, 83, 81,......... 3

Who guarantee that there will be a column with two primes?

Ludovicus

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.
6/19/12 Brian Q. Hutchings