-- Starting with 1 and spiralling anticlockwise in the following way, a square spiral with side length 7 is formed.
--
-- 37 36 35 34 33 32 31
-- 38 17 16 15 14 13 30
-- 39 18  5  4  3 12 29
-- 40 19  6  1  2 11 28
-- 41 20  7  8  9 10 27
-- 42 21 22 23 24 25 26
-- 43 44 45 46 47 48 49
--
-- It is interesting to note that the odd squares lie along the bottom right diagonal, but what is more interesting is that 8 out
-- of the 13 numbers lying along both diagonals are prime; that is, a ratio of 8/13 ≈ 62%.
--
-- If one complete new layer is wrapped around the spiral above, a square spiral with side length 9 will be formed. If this process
-- is continued, what is the side length of the square spiral for which the ratio of primes along both diagonals first falls below
-- 10%?
module Main where

import Euler

-- diagonals of an m by m spiral; m = 2*n + 1.
allDiags = 1 : zipWith (+) allDiags (concat $ map (replicate 4) [2,4..])
allDiags' = map isPrime allDiags
diags' n = take (4*n+1) allDiags'

main = print $ head $ [ 2*n+1 | n <- [1..], (length (filter id (diags' n)) % (4*n+1)) < (1 % 10) ]