Madhur
Posts:
2
Registered:
6/19/12
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Re: Vindication of Goldbach's conjecture
Posted:
Jun 19, 2012 12:46 PM
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On Wednesday, 6 June 2012 21:10:40 UTC+5:30, mluttgens wrote:
> 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.
>
> 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 prime numbers, the even number 26 is necessarily
> the sum of two primes.
> 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 6, 2012)
Goldback figured out that much first ... and that is why it goes by the name of Goldback's Conjecture.
Like you Goldback couldn't prove it ... hence it doesn't go by the name of Goldback's theorem by Goldback's conjecture.
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