import Data.List
 
pairs ((x:xs):ys:t) = (x : union xs ys) : pairs t
 
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
 
iSqrt :: Integer -> Integer
iSqrt = floor . sqrt . (fromIntegral :: Integer -> Double)
-- isPrime n = n == head (primeFactors n)
isPrime n = (and (map f [3, 5..iSqrt n])) && (n `mod` 2) /= 0
    where f x = (n `mod` x) /= 0
 
--uses fastest algorithm I could find for prime number generation
p50 = p (filter (<= 1000001) primesTMWE) 2 2
    where p [] _ z             = z
          p (x:xs) a z
           | isPrime (x + a)   = p xs (x + a) (x + a)
           | otherwise         = p xs (x + a) z
 
main = do
    putStrLn $ show p50