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module AufgabeFFP2
where
-- 1
primes :: [Integer]
primes = sieve [2 ..]
-- sieve of eratosthenes (according to lecture slides)
sieve :: [Integer] -> [Integer]
sieve (x:xs) = x : sieve [ y | y <- xs, mod y x > 0]
-- generate all pairs with map and then filter only the valid ones
-- TODO: filtering should be optimized, still a bit slow
pps :: [(Integer, Integer)]
pps = filter validPair $ map (\x -> (x,x+2)) primes
where
-- pair is valid if the second component n is a prime
-- since simply checking if the Integer is element of the prime-list
-- does not terminate for non-primes, we take the first n primes
validPair :: (Integer,Integer) -> Bool
validPair (_,maybePrime) = elem maybePrime $ take (fromInteger maybePrime) primes
-------------------------------------------------------------------------------
-- 2
-- generates powers of 2
pof2s :: [Integer]
pof2s = [1] ++ (map (2*) pof2s)
pow :: Int -> Integer
pow 0 = 1
pow n = pow (n-1) + pow (n-1)
-- uses memtable for power-calculation
powFast :: Int -> Integer
powFast 0 = 1
powFast n = pof2s !! (n-1) + pof2s !! (n-1)
-------------------------------------------------------------------------------
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