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{-
- Solution to Project Euler problem 58
- Copyright (c) Project Nayuki. All rights reserved.
-
- https://www.nayuki.io/page/project-euler-solutions
- https://github.com/nayuki/Project-Euler-solutions
-}
import Data.Ratio ((%))
import qualified EulerLib
{-
- From the diagram, let's observe the four corners of an n * n square (where n is odd).
- It's not hard to convince yourself that:
- * The bottom right corner always has the value n^2.
- Working clockwise (backwards):
- * The bottom left corner has the value n^2 - (n - 1).
- * The top left corner has the value n^2 - 2(n - 1).
- * The top right has the value n^2 - 3(n - 1).
-
- Furthermore, the number of elements on the diagonal is 2n - 1.
-}
target = 1 % 10
main = putStrLn (show ans)
ans = compute 0 1
compute :: Integer -> Integer -> Integer
compute numPrimes n = let newNumPrimes = numPrimes + (sum [1 | i <- [0..3], EulerLib.isPrime (n^2 - i * (n - 1))])
in if (n > 1 && newNumPrimes % (n * 2 - 1) < target) then n
else compute newNumPrimes (n + 2)