#truncatable

Stop That!

A mathcomic for Sophia Wood’s #mathober theme “truncate.” There must be a name for these primes. 

The number 3797 has an interesting property. Being prime itself, it is possible to continuously remove digits from left to right, and remain prime at each stage: 3797, 797, 97, and 7. Similarly we can work from right to left: 3797, 379, 37, and 3.

Find the sum of the only eleven primes that are both truncatable from left to right and right to left.

NOTE: 2, 3, 5, and 7 are not considered to be truncatable primes.

import Data.Char truncationL xs | length xs > 0 = xs:(truncationL $ tail xs) | otherwise = [] truncationR xs | length xs > 0 = xs:(truncationR $ take ((length xs)-1) xs) | otherwise = [] fromDigits = foldl addDigit 0 where addDigit num d = 10*num + d isPrime :: Int->Bool isPrime x = if x == 1 then False else null [y | y<-[2..floor (sqrt (fromIntegral x))], x `mod` y == 0] isTruncatablePrime n = all (\e -> isPrime $ fromDigits e) (truncationL $ map digitToInt $ show n) && all (\e -> isPrime $ fromDigits e) (truncationR $ map digitToInt $ show n) truncatablePrimes :: [Int] truncatablePrimes = [ x | x<-[11..(10^6)], isTruncatablePrime x] main = print(foldl (+) 0 truncatablePrimes)