# Euler Problem 124 – Prime Factors

When I was looking for a picture to represent Prime Number Factorization, I had no idea what to use. So I Googled images on the topic and discovered there was a Star Trek: Voyager episode called Prime Factors. The above picture is a scene from it — exciting I know! ðŸ˜‰ Too bad its not a picture of Seven of Nine.

So my solution consist of two parts. A prime number generator. I re-used the code from my solution of Euler Problem 131. The other part is a factorization routine that matches against the list of prime numbers. I found some concise Haskell code here.

This routine runs in less than 4 seconds on a single core 3 Ghz system.

``` import Data.List import Data.List.Ordered primes :: Integer -> [Integer] primes m = 2 : sieve [3,5..m] where sieve [] = [] sieve (p:xs) = p : sieve (xs `minus` [p*p, p*p+2*p..m]) primeFactors :: Integer -> [Integer] primeFactors x = unfoldr findFactor x where first (a,b,c) = a findFactor 1 = Nothing findFactor b = (\(_,d,p)-> Just (p, d)) \$ head \$ filter ((==0).first) \$ map (\p -> (b `mod` p, b `div` p, p)) \$ primes 100000 rad :: Integer -> Integer rad n = product \$ Data.List.nub \$ primeFactors n main = print \$ snd \$ sort [(rad x, x) | x <- [1..100000]] !! (9999) ```

Ah, what the heck — Why not?