problem027.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.

from common_funcs import answer, is_prime

def solve():
    greatest = 0
    for a in range(-1000,1000):
        for b in range(-1000,1000):
            n = 0
            while(is_prime(n**2 + a*n + b)):
                n = n + 1
            if n > greatest:
                greatest = n
                best_a = a
                best_b = b
    return best_a * best_b
            
answer(solve)