Solution
The sum of three odd numbers is always odd, but 30 is even, so one of the three primes must be the only even prime 2. The other two primes must then add up to 28, and the only prime pairs with sum 28 are 5 and 23, and 11 and 17. So the sets are $$\{2, 5, 23\}$$ and $$\{2, 11, 17\}$$, which means there are 2 such sets.
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