## Problem:

Euler discovered the remarkable quadratic formula:

n² + n + 41

It turns out that the formula will produce 40 primes for the consecutive values n = 0 to 39. However, when n = 40, 402 + 40 + 41 = 40(40 + 1) + 41 is divisible by 41, and certainly when n = 41, 41² + 41 + 41 is clearly divisible by 41.

The incredible formula n² [−] 79n + 1601 was discovered, which produces 80 primes for the consecutive values n = 0 to 79. The product of the coefficients, [−]79 and 1601, is [−]126479.

n² + an + b, where |a| [<] 1000 and |b| [<] 1000

where |n| is the modulus/absolute value of n
e.g. |11| = 11 and |[−]4| = 4

Find the product of the coefficients, a and b, for the quadratic expression that produces the maximum number of primes for consecutive values of n, starting with n = 0.

-59231

## Code: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;
}
}

}