Question 403907
None. Here's why:


If all three primes a, b, c are odd, then the sum of any two of them is a sufficiently large multiple of 2, not prime. If two of them are odd, then their sum is also even. However, if one or none of the primes are odd, this implies that at least two of a, b, c are equal to 2, and their sum is 4, which is also not a prime. Therefore there are no such sets.