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Vindication of Goldbach's conjecture
Posted:
Jun 6, 2012 11:40 AM
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Vindication of Goldbach's conjecture
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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)
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