-- Considering quadratics of the form:
--
--   n² + 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.

import Euler

nPrimes a b = length $ takeWhile isPrime $ map (\n -> n^2 + a*n + b) [0..]

main = print $ uncurry (*) $ snd $ maximumBy (compare `on` fst) $
       [ (n, (a, b))
       | a <- [-999..999]
       , b <- [-999..999]
       , isPrime (40^2 + a*40 + b)
       , isPrime (30^2 + a*30 + b)
       , let n = nPrimes a b
       ]