**Problem:**

It is possible to write ten as the sum of primes in exactly five different ways:

7 + 3

5 + 5

5 + 3 + 2

3 + 3 + 2 + 2

2 + 2 + 2 + 2 + 2

What is the first value which can be written as the sum of primes in over five thousand different ways?

7 + 3

5 + 5

5 + 3 + 2

3 + 3 + 2 + 2

2 + 2 + 2 + 2 + 2

What is the first value which can be written as the sum of primes in over five thousand different ways?

**Solution:**

-59231

**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 27

* By Nayuki Minase

*

* http://nayuki.eigenstate.org/page/project-euler-solutions

* https://github.com/nayuki/Project-Euler-solutions

*/

public final class p027 implements EulerSolution {

public static void main(String[] args) {

System.out.println(new p027().run());

}

public String run() {

int bestNum = 0;

int bestA = 0;

int bestB = 0;

for (int a = -1000; a <= 1000; a++) {

for (int b = -1000; b <= 1000; b++) {

int num = numberOfConsecutivePrimesGenerated(a, b);

if (num > bestNum) {

bestNum = num;

bestA = a;

bestB = b;

}

}

}

return Integer.toString(bestA * bestB);

}

private static int numberOfConsecutivePrimesGenerated(int a, int b) {

for (int i = 0; ; i++) {

int n = i * i + i * a + b;

if (n < 0 || !Library.isPrime(n))

return i;

}

}

}

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