Question 98948: can the sum of two prime mubers be a prime number?
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! There is only one case where this would happen
Add 2 and 3 (which are both prime) to get 5 (which is prime also). Otherwise, you would always add to an nonprime number. Remember every prime is odd (except 2). Also when two odd numbers are added up, they result in an even number (which is never prime). So the only time when 2 prime numbers add to get a prime number is when the two numbers are 2 and 3.
Update: Someone messaged me and helped point out that there are other cases. So I apologize. It turns out that we have cases like this
5+2 = 7
2+29 = 31
17+2 = 19
which are cases of Twin Primes
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