Question

any even number greater than 2 can be expressed as the sum of two prime numbers?(if yes provide solution if no then why?)

Answer 1

Since four is the only even number greater than two that requires the even prime 2 in order to be written as the sum of two primes, another form of the statement of Goldbach's conjecture is that all even integers greater than 4 are Goldbach numbers.

Answer 2

No any even number greater than 2 cannot be expressed as a sum of two prime numbers.

4 = 2 * 2

6 = 2 * 3

8 = 2 * 2 * 2 ; which is three prime numbers

10 = 2 * 5

12 = 2 * 2 * 3 ; which is also three prime numbers