performance - My Haskell Solution to Euler #3 is Inefficient -

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i attempting solve euler problem 3 in haskell, involves finding largest prime factor of number. code runs long time , seems hang. causing code grossly inefficient?

primes = sieve (2:[3,5..])  sieve (x:xs) = x:[y | y <- (sieve xs), mod y x /= 0]        sieve [] = [] primefactors n = filter (\x -> mod n x == 0) (primesunder n)  primesunder z = reverse (takewhile (< z) primes) solve3 = head (primefactors 600851475143)

your main problem you're checking enormous primes -- way 600851475143. can improve things lot observing 2 things:

  1. every time find prime, can decrease maximum prime @ dividing away factor.
  2. you have primes until reach square root of target. if primes bigger that, , know there no smaller factors, you're done.

using these 2 improvements together, without nicety used of checking primes divisibility, makes program run in snap:

factor = go (2:[3,5..])     go (p:ps) n         | p*p > n        = [n]         | n `mod` p == 0 = p : go (p:ps) (n `div` p)         | otherwise      = go ps n main = print . last . factor $ 600851475143

in ghci:

*main> main 6857 (0.00 secs, 0 bytes)

you can see had inspect numbers 6857 -- 8 orders of magnitude smaller have approach.

independently, sieve dog slow. have at wiki ideas how find primes quickly.


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