Find the next prime number — flow control of nested `for` loops
Factor out the inner loop into a method (not just for the sake of structure, but because it is a method bool is_next_prime(int testNum)):

    for (...) {
        if (testNum % prime) == 0)
            return false;
    }
    return true;


Then

    int getNextPrime() {
        int testNum = primeList.get(primeList.size() - 1) + 2;
        while (!is_next_prime(testNum)) {
            testNum += 2;
        }
        return testNum;
    }