Who can prove that the sum of two primes is even?

Who can prove that the sum of two primes is even?

The sum of two primes greater than 2 is equal to even. This is an obvious conclusion
Because the definition of prime is: except for 1 and itself, can not be divided by other integers
The sum of two odd numbers is equal to even, which proves the conclusion

Help me prove that any even number greater than 2 can be the sum of two prime numbers

This mathematician should not be able to
This seems to be a guess now

Natural reasoning system proves that even numbers can be divisible by 2. 6 is even, so 6 can be divisible by 2

Even numbers are defined as:
Concept: in integers, the number divisible by 2 is even (it's called even number), otherwise it's odd (it's called singular number)
This is a two-way proposition
Any questions?