Project Euler > Problem 57 > Square root convergents (Java Solution)

Problem:

It is possible to show that the square root of two can be expressed as an infinite continued fraction.

[√] 2 = 1 + 1/(2 + 1/(2 + 1/(2 + ... ))) = 1.414213...

By expanding this for the first four iterations, we get:

1 + 1/2 = 3/2 = 1.5
1 + 1/(2 + 1/2) = 7/5 = 1.4
1 + 1/(2 + 1/(2 + 1/2)) = 17/12 = 1.41666...
1 + 1/(2 + 1/(2 + 1/(2 + 1/2))) = 41/29 = 1.41379...

The next three expansions are 99/70, 239/169, and 577/408, but the eighth expansion, 1393/985, is the first example where the number of digits in the numerator exceeds the number of digits in the denominator.

In the first one-thousand expansions, how many fractions contain a numerator with more digits than denominator?

Solution:

104743

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

public interface EulerSolution{

public String run();

}

/** 

 * Solution to Project Euler problem 7
 * By Nayuki Minase
 * 
 * http://nayuki.eigenstate.org/page/project-euler-solutions
 * https://github.com/nayuki/Project-Euler-solutions
 */


public final class p007 implements EulerSolution {
 
 public static void main(String[] args) {
  System.out.println(new p007().run());
 }
 
 
 public String run() {
  for (int i = 2, count = 0; ; i++) {
   if (Library.isPrime(i)) {
    count++;
    if (count == 10001)
     return Integer.toString(i);
   }
  }
 }
 
}