-- 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=40,402+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 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.

module P027 (p027) where

import Data.Function (on)
import Data.List (maximumBy)
import ProjectEuler (isPrime)

findLengthPrimeSequence :: Int -> Int -> Int
findLengthPrimeSequence a b = length $ takeWhile isPrime [n * n + a * n + b | n <- [0 ..]]

findCoefficients =
  let as = [-999 .. 999]
      bs = filter isPrime [2 .. 1000]
      cs = [(a, b) | a <- as, b <- bs]
   in fst $ maximumBy (compare `on` snd) [(c, l) | c <- cs, let l = uncurry findLengthPrimeSequence c]

p027 :: IO ()
p027 = do
  let coefficients = findCoefficients
      result = uncurry (*) coefficients
  putStrLn $
    "Project Euler, Problem 27\n"
      ++ "Answer: "
      ++ show result