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Re: Vindication of Goldbach's conjecture
Posted:
Jun 17, 2012 5:20 AM
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On 16 juin, 20:25, Gus Gassmann <horand.gassm...@googlemail.com>
wrote:
> On Jun 16, 1:08 pm, mluttgens <lutt...@gmail.com> wrote:
>
>
>
>
>
> > On 14 juin, 16:24, Gus Gassmann <horand.gassm...@googlemail.com>
> > wrote:
>
> > > On Jun 14, 6:28 am, mluttgens <lutt...@gmail.com> wrote:
>
> > > > On 10 juin, 00:20, rich...@cogsci.ed.ac.uk (Richard Tobin) wrote:
>
> > > > > In article <0b8c04e9-f6c1-48c0-8f63-c115150dd...@f30g2000vbz.googlegroups.com>,
>
> > > > > 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.
>
> > > It appears you do not even understand the problem. How do you *KNOW*
> > > that you will never miss an even number using this schema? It is fine
> > > and good to verify that every even integer less than 47 can be written
> > > as a sum of two primes, but what about 83749105938571693046? Your
> > > method says nothing about that number.
>
> > 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.
>
> > Thus, it would be ridiculous to try a number as big as
> > 83749105938571693046
>
> So does the number I gave you have a representation as the sum of two
> primes? And what are the two primes? (I must insist on a primality
> proof.) Give me any representation. Should be easy, since you have so
> many to choose from, right?
>
83749105938571693046 = 157 + 83749105938571692889
= 277 + 83749105938571692769
= 283 + 83749105938571692763
= 487 + 83749105938571692559
etc... etc... etc...
Marcel Luttgens
>
> > Here is an example where N is greater then 26:
>
> > Example: N = 138 and N-3 = 135
> > ______________________________
>
> > The relevant primes p are
>
> > 3 5 7 11 13 17 19 23 29
> > 31 37 41 43 47 53 59 61 67 71
> > 73 79 83 89 97 101 103 107 109 113
> > 127 131
>
> > N-p =
>
> > 135 133 131 127 125 121 119 115 109
> > 107 101 97 95 91 85 79 77 71 67
> > 65 59 55 49 41 37 35 31 29 25
> > 11 7
>
> > Thus N = 5+133, 7+131, 11+127, 29+109, 31+107, etc...
>
> > Marcel Luttgens
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