[Haskell-beginners] Question about time consume when calculate prime numbers

[Darren Grant]

On Wed, Sep 12, 2012 at 1:06 AM, Yi Cheng <chengyidna at gmail.com> wrote:
> Recently, I'm trying to solve some problems in project euler using haskell.
> When it came to problem 10, calculating the sum of all primes below
> 20000000, I try to write a program which can generate primes.
> In my memory Eratosthenes is faster than just whether a number can be
> divided by the number less then the square root of it.
> Firstly, I wrote the following programs:
>
> module Main where
> isPrime x = isPrime' 3 x (round . sqrt. fromIntegral $ x)
> isPrime' d target maxd
>   | d > maxd = True
>   | mod target d == 0 = False
>   | otherwise = isPrime' (d + 2) target maxd
>
> main = print $ (sum (filter isPrime [3,5..2000000]) + 2)
>
> And it consume about 11s in my computer.
> Then, I tried to figure out how to solve the problem by Eratosthenes, but
> failed. Later, I find a program implemented by others, meeting my purpose
> and I've used it to solve the problem:
>
> primes :: [Int]
> primes = primes' [2..]
>
> primes' :: [Int] -> [Int]
> primes' [] = []
> primes' (n:ns) = n : primes' (filter (\v -> v `mod` n /= 0) ns)
>
> solve x = sum $ primes' [2..x]
>
> main = print $ solve 2000000
>
> Well, although the code is beautiful, it is slow. Even waiting for a minute,
> no answer was printed.
>
> In C version, Eratosthenes is faster than the method implemented in my
> earlier code, which only consume 0.3s(the earlier method consume 1.6s).
>
> So I want to know, why Eratosthenes implemented in Haskell is slow than the
> ugly code implemented by me.
> Could anyone tell me?
>
>
> Thank you
> Yi Cheng
>
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I attempted this problem as well and noticed similar results. I am
also interested in the performance characteristics of Haskell
solutions and their explanations.

Cheers,
Darren