Euler discovered the remarkable quadratic formula: n2 + 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 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 n = 0 to 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.
The aim is to 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.