How to determine if a number is prime

Your method for finding if your number is prime is the correct method.
To make it so that it does not consistently print out whether or not the number is prime, you could have an external variable, which represents whether or not the number is prime.

Such as

    boolean prime = true;
    for (int p = 2; p < sum; p++) {
        if (sum % p == 0) {
            prime = false;
            break;
        }
    }
    if (prime)
        System.out.println("The sum is a prime number.");
    else
        System.out.println("The sum is not a prime number.");

By doing this method the program will assume the number is prime until it proves that wrong. So when it finds it is not prime it sets the variable to false and breaks out of the loop.

Then after the loop finishes you just have to print whether or not the number was prime.

A way that you could make this loop faster is to go from when p = 2 to when p = the square root of sum. So using this method your for loop will look like this:

    double sq = Math.sqrt((double)sum);
    for (int p = 2; p < sq; p++) {
        //Rest of code goes here
    }

Hope this helps