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. ---------------------------------------------------------------------------------------------- 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 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.