Euler discovered the remarkable quadratic formula:
n^2 + n + 41
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=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 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
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.
$ make euler27 --quiet && ./euler27