Goldbach’s conjecture proven

By me Wadï Mami

Date : 30/10/2025

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 k k <= p < =2k (i)

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

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

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

(B) sum p+q is an even number because p+q = 3k or p+q = 2k and k is even then by correlation

We can state as we have (A) and (B) : every even natural number greater than 2 is the sum of 2 prime numbers.

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

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