Euler Project: Problem 27

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 certainly 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

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 Data.Numbers.Primes
import Data.List
import Data.Ord 

main :: IO()
main = print $ snd $ maximumBy (comparing fst) quadraticPair 

quadraticPair :: [(Int, Int)]
quadraticPair = [(quadraticLength a b, quadraticProduct a b) | a <- [(-1000)..1000], b <- [(-1000)..1000]] 

quadraticProduct :: Int -> Int -> Int
quadraticProduct a b = a*b 

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

*Main> main
-59231