/* OUTPUT:
true
false

2
17
41
1237
*/

// This program deals with prime numbers (no factors other than 1 and itself)
// and relatively prime numbers (pairs that share no common factors).
public class Primes {
    public static void main(String[] args) {
        System.out.println(relativelyPrime(9, 16));
        System.out.println(relativelyPrime(15, 25));
        System.out.println();
        
        System.out.println(nextPrime(2));
        System.out.println(nextPrime(14));
        System.out.println(nextPrime(38));
        System.out.println(nextPrime(1234));
    }
    
    // Returns true if the given two numbers do not have any factors in common.
    //                                         9      16
    public static boolean relativelyPrime(int n1, int n2) {
        for (int i = 2; i <= Math.min(n1, n2); i++) {
            if ((n1 % i == 0) && (n2 % i == 0)) {
                return false;
            }
        }
        
        return true;
    }
    
    // Returns the next prime number that is greater than or equal to n.
    public static int nextPrime(int n) {
        /*
        start at n
        check if it is prime
            if so, stop
            if not, go to the next number
        */
        while (!isPrime(n)) {
            n++;
        }
        return n;
    }
    
    // Returns true if the given number n is prime (has no factors other than 1 and itself).
    public static boolean isPrime(int n) {
        /* less elegant solution #1:
        int factors = numFactors(n);
        if (factors <= 2) {
            return true;
        } else {
            return false;
        }
        */
        
        /* solution #2:
        int factors = numFactors(n);
        return (factors <= 2);
        */
        
        // shortest solution
        return (numFactors(n) <= 2);
    }
    
    // Returns the number of factors that the given n has.
    public static int numFactors(int n) {
        // cumulative sum
        int count = 0;
        for (int i = 1; i <= n; i++) {
            if (n % i == 0) {
                // i is a factor of n
                count++;
            }
        }
        return count;
    }
}














/*
System.out.println

*/