Goldbach Conjecture!

Goldbach Conjecture states that" Every even integer greater than 2 can be written as sum of two primes"

I think this might be a proof.

Let a number be 2k and let the two primes be 2n+1 and 2m+1. Therefore, 2k=2(m+n+1) k=m+n+1

Therefore, there are infinite many solutions and one of them satisfies the given equation. Goldbach conjecture is true. All who think this is wrong , please comment and make me realize my mistake

#NumberTheory

Easy Math Editor

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Comments

What is n and m? How do you determine them for a given k? E.g. If $k = 1000000000$ , what is $n, m$ ?

Calvin Lin Staff - 6 years, 4 months ago

I meant that prime is odd, so they can written in the form of 2n+1 and 2m+1. By the conjecture, let the sum of two numbers is a even number 2k=2m+2n+2 that is equal to k=m+n+1

Sudhir Aripirala - 6 years, 4 months ago

I understood my mistake @Calvin Lin

Sudhir Aripirala - 5 years, 1 month ago

That's great! Understanding your own mistakes is the first step towards discovering new facts!

Calvin Lin Staff - 5 years, 1 month ago

You can find infinitely many solutions for some random m and n. But how do you know you can find infinitely many solutions such that 2m + 1 and 2n + 1 are both prime?

Sandhya Saravanan - 5 years, 9 months ago

there are infinite but only one satisfies it

Sudhir Aripirala - 5 years, 9 months ago

How do you know that there will be one for sure that will satisfy it? What if there are none?

Sandhya Saravanan - 5 years, 9 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$