27.Quadratic Expression

Euler published 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.

Using computers, 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.

public class Problem27 {
    public void quadratic() {
        Problem7 p7 = new Problem7();
        int maxp = 0, af=0,bf=0;
        for (int a=-999;a<1000;a++) {
            for (int b=-999;b<1000;b++) {
                int n=0;
                while(true){
                    long qf = n*n+n*a+b;
                    if (p7.isPrime(Math.abs(qf))) {
                        n+=1;
                    } else {
                        if (n>maxp) {
                            maxp = n;
                            af=a;
                            bf=b;
                        }
                        break;
                    }
                }
            }
        }
        long mqf = maxp*maxp+maxp*af+bf;
        System.out.println((af*bf);
    }

    public static void main(String[] args) {
        Problem27 p = new Problem27();
        p.quadratic();
        }
}
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