Project Euler Problem #027: Quadratic primes

(Problem Link)

Euler discovered the remarkable quadratic formula:

<div align="center">n ^ 2 + n + 41</div>

It turns out that the formula will produce 40 primes for the consecutive integer values 0 <= n <= 39. However, when n = 40, 40 ^ 2 + 40 + 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 0 <= n <= 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.

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<p align="center"> A massive collaborative effort by <a href="https://github.com/OpenGenus/cosmos">OpenGenus Foundation</a> </p>

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