primes7 - iterate TD by segments - http://stackoverflow.com/questions/16570644/last-init-faster-than-head-tail/16598738#16598738

gistfile1.hs

primes4 :: [Integer]
primes4 = iterate
        (\p -> ([x |
                x <- [p + 1 ..],
                all (\p -> x `mod` p /= 0) $
                    takeWhile (\p-> p*p <= x) primes4 ] !! 0)
            )
        2

primes5 :: [Integer]
primes5 = 2 : iterate (\p -> head [x | x <- [p + 2, p + 4 ..],
                               all (\p -> x `mod` p /= 0) $ tail $
                                 takeWhile (\p-> p*p <= x) primes5]) 3             --  n^2.0

primes6 :: [Integer]
primes6 = 2 : iterate (\p ->                     -- slower 2x, interpreted, with "and"
                head [x | x <- [p + 2, p + 4 ..],
                  and [ rem x p /= 0 | p<- takeWhile ((<= x).(^2)) $ tail primes6]]) 3


-- why not more than just head, actually? ... 

primes7a :: [Integer]
primes7a = concatMap snd $
            iterate (\((n,p:ps@(q:_)),_) -> ((n+1,ps),
              [x | x <- [p*p + 2, p*p + 4 .. q*q - 2],
                   all ((/= 0).rem x) $ take n $ tail primes7a]))    -- 50k: 1.91 secs  n^1.4
            ((1,tail primes7a),[2,3,5,7]) 

primes7 :: [Integer]
primes7 = concatMap snd $
            iterate (\((n,p:ps@(q:_)),_) -> ((n+1,ps),           -- 50k: 1.70s secs  n^1.4
                [x | let lst = take n $ tail primes7,
                     x <- [p*p + 2, p*p + 4 .. q*q - 2],
                     all ((/= 0).rem x) $ lst]))
            ((1,tail primes7),[2,3,5,7])