Effectively you have three parts to this problem.
1. Get a list of numbers
2. Iterate over the list
3. Check to see if the number is prime
Let's ignore the first step as you should easily be able to do this. This leaves you with the iterate and check to see if the number is a prime. Obviously, the most complicated part of this is the prime number check so you want to simplify this as much as possible. Fortunately, there are a number of well known prime generation techniques some of which are exceedingly efficient. What I would be tempted to do to solve this is find the largest number in the list first. Once you have the largest number, use a technique such as the
Sieve of Eratosthenes[
^] to generate all of the possible prime numbers up to that point. Iterate over your list again and check to see if the number is in the sieve you just generated. The beauty about this approach is that techniques such as sieves are relatively fast so you can throw in reasonably large numbers and calculate whether or not it's prime with ease.
As a bonus, you could be really sneaky and pre-generate every prime up to the maximum int size and use that list every time.