{-# OPTIONS_GHC -O2 -fno-cse #-}
primesTMWE = 2:3:5:7: gapsW 11 wheel (joinT3 $ rollW 11 wheel primes')
  where
    primes' = 11: gapsW 13 (tail wheel) (joinT3 $ rollW 11 wheel primes')
 
gapsW k ws@(w:t) cs@(c:u) | k==c  = gapsW (k+w) t u 
                          | True  = k : gapsW (k+w) t cs  
rollW k ws@(w:t) ps@(p:u) | k==p  = scanl (\c d->c+p*d) (p*p) ws 
                                      : rollW (k+w) t u 
                          | True  = rollW (k+w) t ps    
joinT3 ((x:xs): ~(ys:zs:t)) = x : union xs (union ys zs)    
                                   `union` joinT3 (pairs t)  
wheel = 2:4:2:4:6:2:6:4:2:4:6:6:2:6:4:2:6:4:6:8:4:2:4:2:
        4:8:6:4:6:2:4:6:2:6:6:4:2:4:6:2:6:4:2:4:2:10:2:10:wheel
 
main = mapM_ print 
         . take 10 . map fst 
         . tail . iterate (splitAt 10.snd)
         $ ([],take 100 primesTMWE)
 
pairs ((x:xs):ys:t) = (x : union xs ys) : pairs t 
union (x:xs) (y:ys) = case (compare x y) of 
           LT -> x : union  xs  (y:ys)
           EQ -> x : union  xs     ys 
           GT -> y : union (x:xs)  ys
 

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