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Consider that every prime number except 2 is an odd number.

Consider also that the sum of two odd numbers is always an even number.

Thus, the only case in which an odd number can be expressed as the sum of two primes is when it is 2 greater than a prime number, since it can take advantage of the only even Prime number, 2.

For example, 21 can be expressed as 2+19, both of which are primes. However, 27 has no such two primes, since 25 is not prime (5x5=25).

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Q: Can every odd number greater than 3 be written as the sum of two prime numbers?
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