We know that (odd number)+(even number) always, no matter what, equals an odd number.
Since all even numbers apart from 2 are composite, There are only one solution left.
Quick calculations show that 27-2=25 and 25 is NOT a prime number.
Therefore, 27 cannot be written as a sum of 2 primes no matter what.
Congratulations to Leon Shinka for the first correct solution! And to the many others who sent in a correct solution.