[Math] Is there way to know if ODD number can be expressed as sum of two primes

Question

I'm solving problem and I need your help, I know that every even integer can be expressed as sum of two primes and every integer can be expressed as sum of three primes. (for all integers <= 2 * 10^9)

But I want to know is there a way to check can we express odd number as sum of two primes.

Thanks in advance.

Answer 1

Sure; if $n-2$ is prime, then yes, otherwise not.

Adding two numbers to get an odd number requires that one of them is odd and the other even, but since there is only one even prime ($2$), the test is simple.