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 actually, works as advertised.

Best,

On 12 March 2010 21:14, legajid <legajid@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 ?

Thanks for your help,

Didier.




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