Ozgur Akgun ozgurakgun at gmail.com
Fri Mar 12 22:49:24 EST 2010

```If we try to implement your idea literally we would need one more parameter
to the function: the list of existing primes.
I'll call this function primesWRT, since it finds all primes, with respect
to the second list provided.

primesWRT [] _ = []    -- base case
primesWRT (x:xs) existing
-- if all x is not divided by all of the existing primes,
-- x itself is a prime (wrt 'existing')
-- add it to the primes list, and the existing primes list for the next
function call
| all (\ y -> mod x y /= 0 ) existing = x : primesWRT xs (x:existing)
-- if x is not prime, check the rest.
| otherwise = primesWRT xs existing

primes xs = primesWRT xs []

Please keep in mind that this function assumes its parameter to be in form
[2..n]. But this is an assumption coming from your description.

primes [2..20] = [2,3,5,7,11,13,17,19]
primes [2..30] = [2,3,5,7,11,13,17,19,23,29]
primes [10..30] = [10,11,12,13,14,15,16,17,18,19,21,23,25,27,29] -- not bad

Best,

On 12 March 2010 21:14, legajid <legajid at free.fr> wrote:

> Hi,
> i'm trying to write a function to find all primes from 2 to N.
>
>
> 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.
> f needs g that needs f : what's wrong with my mind ?
> Perhaps i am still under control of imperative programming ?
>
>
> Didier.
>
>
>
>
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