Prime numbers that are sums of Prime numbers themselves

Question

what is the minimum prime number that is the sum of exactly two odd prime numbers?

i.e I want to find a counter example to:

$$p_i+p_j \in \mathbb P \operatorname{iff} i=1 \lor j=1$$

Answer 1

Sum of two odd primes is even, which means that it cannot be a prime > 2.