Project Euler > Problem 127 > abc-hits (Java Solution)

Problem:

The radical of n, rad(n), is the product of distinct prime factors of n. For example, 504 = 23 [×] 32 [×] 7, so rad(504) = 2 [×] 3 [×] 7 = 42.

We shall define the triplet of positive integers (a, b, c) to be an abc-hit if:

1. GCD(a, b) = GCD(a, c) = GCD(b, c) = 1
2. a [<] b
3. a + b = c
4. rad(abc) [<] c

For example, (5, 27, 32) is an abc-hit, because:

1. GCD(5, 27) = GCD(5, 32) = GCD(27, 32) = 1
2. 5 [<] 27
3. 5 + 27 = 32
4. rad(4320) = 30 [<] 32

It turns out that abc-hits are quite rare and there are only thirty-one abc-hits for c [<] 1000, with [∑]c = 12523.

Find [∑]c for c [<] 120000.

Solution:

-59231

Code:
The solution may include methods that will be found here: Library.java .

public interface EulerSolution{

public String run();

}

/* 
 * Solution to Project Euler problem 27
 * By Nayuki Minase
 * 
 * http://nayuki.eigenstate.org/page/project-euler-solutions
 * https://github.com/nayuki/Project-Euler-solutions
 */


public final class p027 implements EulerSolution {
	
	public static void main(String[] args) {
		System.out.println(new p027().run());
	}
	
	
	public String run() {
		int bestNum = 0;
		int bestA = 0;
		int bestB = 0;
		for (int a = -1000; a <= 1000; a++) {
			for (int b = -1000; b <= 1000; b++) {
				int num = numberOfConsecutivePrimesGenerated(a, b);
				if (num > bestNum) {
					bestNum = num;
					bestA = a;
					bestB = b;
				}
			}
		}
		return Integer.toString(bestA * bestB);
	}
	
	
	private static int numberOfConsecutivePrimesGenerated(int a, int b) {
		for (int i = 0; ; i++) {
			int n = i * i + i * a + b;
			if (n < 0 || !Library.isPrime(n))
				return i;
		}
	}
	
}