# Problem 27

Solution to Problem 27. Written in Python.

Problem: 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.