No.
2 and 3.
61 and 23.
17, 53, 71
How about: 199+5 = 204
29 is the answer. 29 is prime. 2+9=11 which is prime. 9-2=7 which is prime.
There are no two numbers whose product is 23 and whose sum is 10. 23 is a prime number, and the only numbers whose product is 23 are 23 and 1. A prime number can only be divided by itself and 1.
3, 5 and 11
37
85
I think it will be 17. The sum of digits is 8, which is the cube of 2.
2 + 3 = 5
53 is prime, and 5+3 = 8.