problem27.py

import math

def is_prime(n):
    if n < 0:
        return False
    for j in range(2, math.sqrt(n)+1):
        if n%j == 0:
            return False
    return True

def generate_primes(n):
    return [x for x in range(2, n+1) if is_prime(x)]

def f(a, b, n):
    return (n**2 + (a*n) + b)

def sequence_of_primes(a, b):
    n = 0
    t = True
    while t:
        t = is_prime(f(a, b, n))
        n += 1
    return n-1

p = generate_primes(1000)

maximum = 0
for i in p:
    for j in p:
        l = sequence_of_primes(i, j)
        if l > maximum:
            maximum = l
            nums = (i, j)
        l = sequence_of_primes(-i, j)
        if l > maximum:
            maximum = l
            nums = (-i, j)

print("n^2 + %dn + %d yields %d primes" % (nums[0], nums[1], maximum))
print("%d" % (nums[0] * nums[1]))