Problem27.py

"""
Euler discovered the remarkable quadratic formula:

n^2 + 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, 41^2 + 41 + 41 is clearly divisible by 41.

The incredible formula  n^2 - 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:

n^2 + 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.
"""
if __name__ == "__main__":
    best_a, best_b, best_n = None, None, 0
    largest_prime = -1
    for a in xrange(-1000, 1001, 1):
        for b in xrange(-1000, 1001, 1):
            from maths.misc import is_prime
            
            prime = True
            n = 0
            while prime:
                result = n*n + a*n + b
                prime = is_prime(abs(result))
                
                if not prime:
                    break
                n += 1
            
            
            if n > best_n:
                best_a, best_b, best_n = a, b, n
    
    print('(a,b) = (%d, %d) with n = %d with a*b=%d'%(best_a, best_b, best_n, best_a*best_b))