GoldBach Conjecture English

 

Resolution of Goldbach's conjecture

February 23, 2026

 

Resolution of Goldbach's conjecture

Author: Wadï Mami

Date :October 30, 2025

Email: wmami@steg.com.tn / didipostman77@gmail.com

Statement of Goldbach's conjecture

"Every even number greater than 2 is the sum of two prime numbers."

A prime number is an odd number, except for 2.

The sum of two odd numbers is an even number.

SO

The sum of two prime numbers is an even number, except  for 2. (A)

It now remains to demonstrate the other meaning of the conjecture.

Based on Erdős' theorem, which he established when he was 18 years old:

For any integer n > 1, there always exists a prime number between n and 2n.

Therefore, there exists a prime number p between n and 2n.

n <= p <= 2n     (I)

and by analogy there exists a prime number q between n/2 and n

n/2 <= q <= n      (II)

(I)            + (II) gives       3n/2 <= p+q <= 3n               

The sum p+q is an even number according to (A). 

p+q = 2k

which gives    3n/2 <= 2k <= 3n

<=>                3n/4 <= k <= 3n/2

<=>                             k =n 

QED 

 

Hence the other meaning of the conjecture: the sum of two prime numbers except 2 is an even number greater than 2. (B)

(A)   And (B) proves the validity of Goldbach's conjecture

"Every even number greater than 2 is the sum of two prime numbers."

 

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