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I was looking into Goldbach Conjecture proof.

Is it proved that we can express any integer as a sum of different primes.

And if yes, Goldbach conjecture says we can do that with even numbers and only two primes...

Isn't Goldbach just a special case of this?

And can we move beyond this and say we can express any number as the sum of Say P primes.

I mean every even number is made up of 2's....

That's prime. Just more than two.

Akhilesh
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  • cf. this; but what about $N=1$? – J. W. Tanner May 18 '20 at 12:09
  • https://math.stackexchange.com/questions/1382663/prove-that-every-integer-n-geq-7-can-be-expressed-as-a-sum-of-distinct-primes – quasi May 18 '20 at 12:11
  • What is your question? If it's "Isn't Goldbach just a special case of this?", the answer is something like "Yes, but that doesn't really tell us anything interesting.". – Mees de Vries May 18 '20 at 12:32
  • Yes-here's an example: 24=19+5=17+7 – P. Lawrence May 18 '20 at 20:07
  • @Sam This has been completely solved in the mean time. So, we can say, that every positive integer greater than $1$ is the sum of at most $4$ (not necessarily distinct) primes. – Peter May 19 '20 at 07:42
  • Every positive integer greater than $1$ is the sum of twos and threes, this is however a quite boring statement. If you want, you con consider Goldbach's conjecture as a strengthening of this statement, in fact the strongest statement of this kind for even numbers. – Peter May 19 '20 at 07:46

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