Goldbach’s conjecture proven

In the name of God, the most gracious, the most merciful

Thanks be to God, Lord of all worlds

Peace and blessings be upon the noblest of messengers.

Goldbach’s conjecture proven

By me Wadï Mami

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

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 except 2

The sum of 2 odd numbers is an even number

Then

The sum of two prime numbers is an even number except 2 (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  3n/2 and upper limit 3n  

f(x) = 3x/2 and g(x) = 3x  the two f(x) and g(x) are linear function the area between them that intersect for x>0 contains points solutions which are sum of p and q prime numbers and their abscissa are x integer > 1. (B)

it remains to proove that h(x) = 2x ( even function for n integer > 2) is all absorbed by the area delimited by f(x) = 3x/2 and g(x) = 3x, all of f(x), g(x) and h(x) are linear functions 

In a linear function, the coefficients are the slope (the coefficient of the independent variable, usually denoted as '

$m$

') and the y-intercept (the constant term, usually denoted as '

$b$

'). The slope represents the rate of change of the dependent variable, while the y-intercept is the value of the dependent variable when the independent variable is zero. 

Slope (m)

 it remains to proove that correspondent angle of h(x) zeta is between alpha angle of f(x) and beta angle of g(x) ie the slope of h(x) is between the slope of f(x) and the slope of g(x) obvious 3/2 <= 2 <= 3

  tangent(alpha) <= tangent(zeta) <= tangent(beta) 

               alpha  <=      zeta           <=              beta  

(B)

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.

-- Minds, like parachutes, function best when open. ,,,

             (o o)

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| Wadï Mami didipostman

| Github : https://www.github.com/didipostman

| e-mail : wmami@steg.com.tn / didipostman77@gmail.com

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