Question

Will adding 3 different prime numbers result in a prime number?

Answer 1

Depends on the prime numbers.

Explanation:

2+3+7=12, 12 is divisible by 3, 4, 6, 2, 1, and 12.

3+7+31=41, 41 is only divisible by 1 and itself.

Answer 2

Well, when you think about it a random set of prime numbers would be 1,3,5,7,11,13...
If you add 1+3+5 you get 9 which isn't a prime number.
Another example is 7+11+13 you get 31 which is a prime number.
So to answer your question: it depends on the type of prime numbers that you use