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:

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


closed as off-topic by Morgan Rodgers, Claude Leibovici, Key Flex, Gibbs, Don Thousand Oct 14 '18 at 13:11

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  • $\begingroup$ If prime numbers are allowed to be negative then the answer is $-2=3+(-5)$ for example. $\endgroup$ – Mark Bennet Oct 13 '18 at 7:16

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

  • $\begingroup$ lol yeah that's not what people said in the chat room the other day $\endgroup$ – Adam Oct 13 '18 at 5:48
  • $\begingroup$ @Adam If the people in the chat room had a way to add two odd numbers together to get a third odd number, you should share. I'd love to see it! $\endgroup$ – Morgan Rodgers Oct 13 '18 at 5:51
  • $\begingroup$ haha no its ok fine ill stop trolling $\endgroup$ – Adam Oct 13 '18 at 6:14

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