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


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)

