In the previous posts, we have gone quite deep in delving and proving some complicated theorems. In this post, we go again the the basics. In this short proof, we show that the sum of two **prime numbers**, both greater than 2 is even.

**Theorem**

The sum of two primes, both greater than 2, is always even.

**Proof**

Let and be prime numbers both greater than 2. Then, both of them are odd numbers. This means that we can let and where and are positive integers. Adding, we have

Factoring out 2, we have

Since is divisible by , it is even. Therefore,

is even.

Therefore, the sum of two primes both greater than 2 is even.

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One mistake in the proof. you write p=2q+1 and next use p=2r+1 . So replace p=2q+1 by p=2r+1.

Thank m asif for pointing out the mistake. Changed it already.