[Haskell-beginners] Primes calculation

[Daniel Fischer]

Am Freitag 12 März 2010 22:14:00 schrieb legajid:
> Hi,
> i'm trying to write a function to find all primes from 2 to N.
>

Many examples at http://www.haskell.org/haskellwiki/Prime_numbers

>
> My idea is :
>     take the first number (2)
>     try to find whether it's a multiple of one of all existing primes
> ([] at first)
>     add 2 to the list of primes
>
>     take the following number (3)
>     find if multiple of existing primes ([2])
>     add 3 to the list of primes
>
>     take the following number (4)
>     find if multiple of existing primes ([2, 3])
>     do not add 4 to the list of primes
>
>     ...
>
>     take the following number (8)
>     find if multiple of existing primes ([2, 3, 5, 7])
>     do not add 8 to the list of primes
>
>     take the following number (9)
>     find if multiple of existing primes ([2, 3, 5, 7])
>     do not add 9 to the list of primes (multiple of 3)
>
>     and so on...
>
> So, i would like a function like :
>
>     f (x : xs)  = g  x  :  f  xs
>
> g would  return  x  if  x is prime, []  otherwise
>
> But g would use the preceding value of  f  (list of primes before  the
> calculation for x) that is a result of g itself.

So g would need the list of primes [found so far] as a parameter (without 
that, it would need to check whether x is prime from scratch).

If you're not committed to performance, what about simple trial division:

trialDivPrime :: [Integer] -> Integer -> Bool
trialDivPrime (p:ps) n 
    = (n < p*p) || (n `mod` p /= 0 && trialDivPrime ps n)

isPrime = trialDivPrime primes

primes = 2:filter isPrime [3, 5 .. ]

If you're after performance, a bit-sieve (STUArray) is what you want.

> f needs g that needs f : what's wrong with my mind ?
> Perhaps i am still under control of imperative programming ?
>
> Thanks for your help,
>
> Didier.