Goldbach's conjecture proof By Wadï Mami

Goldbach's conjecture is one of the oldest and best-known unsolved problems in number theory and all of mathematics. It states that every even natural number greater than 2 is the sum of two prime numbers.

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A prime number must be an odd number

The sum of 2 odd numbers is an even number

Then

The sum of two prime numbers is an even number (A).

Erdös Theorem : For every integer n > 1, it exists always a prime number between n and 2n

(Source : Le Beau livre des Maths De Pythagore à la 57 dimension DUNOD edition, author Clifford A.Pickover)

By récurrence of Erdös Theorem mentioned above and (A)

There is always k even number which is the sum of two prime numbers p and q. (B)

p for n                   n <= p < =2n (i)

q for n/2              n / 2<= q <= n (j)

  (i) + (j)      n + n /2 <= p+q <= 3n ie

                                  3n/2 <= p+q <= 3n wich implies 

 k= p+q is an even number because of (A)  and n integer > 1 and k is between lower limit  n+ n/2 and upper limit 3n  

We can state then every even natural number greater than 2 is the sum of 2 prime numbers

(what needed to be demonstrated) Goldbach’s conjecture proven.