Find the product of the coefficients, a and b, for the quadratic expression (n**2+n+41) that produces the maximum number of primes for consecutive values of n, starting with n=0.

quadratic_primes.py

from math import sqrt


MAX = 999999
sieve = [True] * (MAX + 1)
sieve[0], sieve[1] = False, False

for i in range(2, int(sqrt(MAX)) + 1):
	if sieve[i] is True:
		for j in range(2 * i, MAX, i):
			sieve[j] = False


def len_prime_seq(a, b):
	eqn = lambda n: n ** 2 + a * n + b
	count = 0
	for i in range(0, MAX):
		val = eqn(i)
		if sieve[val] is True:
			count += 1
		else:
			break
	return count

max_len = 0
pair = (0, 0)
for a in range(-999, 999 + 1):
	for b in range(-1000, 1000 + 1):
		len_seq = len_prime_seq(a, b)
		if len_seq > max_len:
			max_len = len_seq
			pair = (a, b)

print(max_len, pair)