Answer:
19 is the smallest prime number that is the sum of three different prime number.
Explanation:
To find this:
2 is the only even prime number and other prime numbers are odd
adding any two prime number always gives even number.
so the least numbers that are required to do is 3,5 and 7; their sum is 15
so any prine number less than 15 is not possible for this question
so, the next prime number is 17
17 minus any other prime no less 17 are13,11,7.5.3,2 give the number that 4,6,10,12,14,15 which are not sum of any two different prime numbers
so the answer is 19=11+5+3.