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

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## Comments

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

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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

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I understood my mistake @Calvin Lin

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

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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?

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there are infinite but only one satisfies it

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

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