29 lines
1.2 KiB
Haskell
29 lines
1.2 KiB
Haskell
-- 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
|
|
|
|
isPrime n = n >= 2 && not (any (\p -> n `mod` p == 0) $ takeWhile ((<= n) . (^2)) primes)
|
|
|
|
-- 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) ]
|