**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.

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.

**Solution:**

142913828922

**Code:**

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

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);

}

}

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