Project Euler > Problem 46 > Goldbach's other conjecture (Java Solution)

Problem:

It was proposed by Christian Goldbach that every odd composite number can be written as the sum of a prime and twice a square.

9 = 7 + 2[×]12
15 = 7 + 2[×]22
21 = 3 + 2[×]32
25 = 7 + 2[×]32
27 = 19 + 2[×]22
33 = 31 + 2[×]12

It turns out that the conjecture was false.

What is the smallest odd composite that cannot be written as the sum of a prime and twice a square?

Solution:

5777

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

public interface EulerSolution{

public String run();

}

/* 
 * Solution to Project Euler problem 46
 * By Nayuki Minase
 * 
 * http://nayuki.eigenstate.org/page/project-euler-solutions
 * https://github.com/nayuki/Project-Euler-solutions
 */


public final class p046 implements EulerSolution {
 
 public static void main(String[] args) {
  System.out.println(new p046().run());
 }
 
 
 public String run() {
  for (int i = 2; ; i++) {
   if (!satisfiesConjecture(i))
    return Integer.toString(i);
  }
 }
 
 
 private boolean satisfiesConjecture(int n) {
  if (n % 2 == 0 || isPrime(n))
   return true;
  
  // Now n is an odd composite number
  for (int i = 1; i * i * 2 <= n; i++) {
   if (isPrime(n - i * i * 2))
    return true;
  }
  return false;
 }
 
 
 private boolean[] isPrime = {};
 
 private boolean isPrime(int n) {
  if (n >= isPrime.length)
   isPrime = Library.listPrimality(n * 2);
  return isPrime[n];
 }
 
}