## Problem:

The smallest positive integer n for which the numbers n2+1, n2+3, n2+7, n2+9, n2+13, and n2+27 are consecutive primes is 10. The sum of all such integers n below one-million is 1242490.

What is the sum of all such integers n below 150 million?

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];	}	}