Project Euler > Problem 27 > Quadratic primes (Java Solution)

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.

Considering quadratics of the form:

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.

Solution:

-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;
  }
 }
 
}