```{-
Copyright (C) 2011 Dr. Alistair Ward

This program is free software: you can redistribute it and/or modify
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.

This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
GNU General Public License for more details.

You should have received a copy of the GNU General Public License
along with this program.  If not, see <http://www.gnu.org/licenses/>.
-}
{- |
[@AUTHOR@]	Dr. Alistair Ward

[@DESCRIPTION@] Generates the constant, conceptally infinite, list of /prime-numbers/, using /Turner's Sieve/; <http://www.haskell.org/haskellwiki/Prime_numbers#Turner.27s_sieve_-_Trial_division>.
-}

-- * Functions
) where

import qualified	Factory.Math.Power	as Math.Power

{- |
* For each /prime/, the infinite list of candidates greater than its /square/,

* CAVEAT: though one can easily add a 'Data.PrimeWheel.PrimeWheel', it proved counterproductive.
-}
turnersSieve :: Integral prime => [prime]
turnersSieve	= 2 : sieve [3, 5 ..]	where
sieve :: Integral i => [i] -> [i]
sieve []			= []
sieve (prime : candidates)	= prime : sieve (
filter (
\candidate	-> any (\$ candidate) [
(< Math.Power.square prime),	--Unconditionally admit any candidate smaller than the square of the last prime.
(/= 0) . (`rem` prime)		--Ensure indivisibility, of all subsequent candidates, by the last prime discovered.
]
) candidates
)

```