What is the smallest prime that is the sum of three different composite numbers?
Let's start by listing composite numbers:
4, 6, 8, 9, 10, 12, 14, 15, 16, ...
4 + 6 + 8 cannot be prime, but 4 + 6 + 9 can.
Also, 19 = 4 + 6 + 9, so the sum is indeed a prime, and the numbers are composite.
The required answer is 19.