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Show that every even natural number grater than $2$ can be expressed as a sum of two prime numbers. No idea how to prove this. Can you help? thanks

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You might want to have a look at this: – Abel May 2 '13 at 14:54
Let me know if you find a proof of this. We can publish it together :-). – user17762 May 2 '13 at 14:55
You are not alone. – Rankeya May 2 '13 at 14:55
Tough course you are taking, if this is homework! Solving it would put you on the front pages of newspapers. – André Nicolas May 2 '13 at 14:59
@AndréNicolas: Some of the conjectures in the past were solved by mistake in the past.(Teachers left them as open problems in home assignments). – Inceptio May 2 '13 at 15:06
up vote 6 down vote accepted

This is known as Goldbach's conjecture. This still remains unproved till date. I bet you will make a great fame if you find the proof. All the best with that.:)

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got it, my lecturer trolled me, didn't know of this conjecture, thanks for link – bateman May 2 '13 at 15:01

Well, it's either the sum of an odd prime +2 or the sum of two odd primes which is always an even number. The sum of an odd prime + 2 is always odd, so we can scratch out the prime 2 and focus on the odd primes.

So then ask, does the combination of all odd primes taken two at a time cover every even number? And the answer is yes.


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