A scalene triangle has side lengths which are prime numbers and the length of its perimeter is also prime. what is its smallest possible perimeter?

The smallest prime numbers are 1, 3 and 7. However they would not work to become a triangle, because the sum of the two shortest sides should be larger than the length of the longest side.  1+3 is less than 7 so it wouldn't work. The next set of prime numbers is 5,7,11 which I think is the answer since 5+7 is more than 11 and 5+7+11 is 23 which is prime.   Answers: 23 is the smallest possible prime perimeter