1. The problem statement, all variables and given/known data If the sum of two primes is prime, then one of the primes must be 2. 3. The attempt at a solution Proof: Since all primes bigger than 2 are odd the only way to get a sum of two primes to be odd is to add an odd prime with an even prime. Let y be an odd prime such that there exists and integer q so that y=2q+1, and then we will add this to 2 giving us a new number k such that k=2+(2q+1)=2q+3 which is not divisible by 2 therefore it is odd. Suppose for the sake of contradiction that both of the primes were odd and when added together were prime. Let integers T and P be given that are odd primes. And T=2s+1 , where s is an integer. And P=2d+1. Now if we add T+P , we get that T+P= (2s+1)+(2d+1)=2s+2d+2=2(s+d+1) , which is divisible by 2 and is not prime by definition and is a contradiction. My proof is kinda choppy and i kinda used 2 methods in the proof. Which would be better, to do a proof by contradiction of a direct proof?