problem 27

"""Euler discovered the remarkable quadratic formula:

n2+n+41
It turns out that the formula will produce 40 primes for the consecutive integer values 0≤n≤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 0≤n≤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.
"""
import math

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

best_a = 0
best_b = 0
max_primes = 1
for a in range(-1000,1000):
  for b in range(-1000,1000):
    length = 0
    while is_prime(length ** 2 + a * length + b):
      length += 1
    if length > max_primes:
      max_primes = length
      best_a = a
      best_b = b
      print(best_a * best_b)