## Problem:

In the following equation x, y, and n are positive integers.

1

x
+
1

y
=
1

n

It can be verified that when n = 1260 there are 113 distinct solutions and this is the least value of n for which the total number of distinct solutions exceeds one hundred.

What is the least value of n for which the number of distinct solutions exceeds four million?

NOTE: This problem is a much more difficult version of problem 108 and as it is well beyond the limitations of a brute force approach it requires a clever implementation.

142913828922

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

public interface EulerSolution{public String run();}
/*  * Solution to Project Euler problem 10 * By Nayuki Minase *  * http://nayuki.eigenstate.org/page/project-euler-solutions * https://github.com/nayuki/Project-Euler-solutions */public final class p010 implements EulerSolution {		public static void main(String[] args) {		System.out.println(new p010().run());	}			private static final int LIMIT = 2000000;		public String run() {		long sum = 0;		for (int p : Library.listPrimes(LIMIT - 1))			sum += p;		return Long.toString(sum);	}	}