51 lines
1.8 KiB
Haskell
51 lines
1.8 KiB
Haskell
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--
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-- The primes 3, 7, 109, and 673, are quite remarkable.
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-- By taking any two primes and concatenating them in any order the result will always be prime.
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-- For example, taking 7 and 109, both 7109 and 1097 are prime.
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-- The sum of these four primes, 792, represents the lowest sum for a set of four primes with this property.
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--
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-- Find the lowest sum for a set of five primes for which any two primes concatenate to produce another prime.
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--
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-- Should use the following property
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-- [x,y,z,t] special <=> [x,y,z] & [x,y,t] & [x,z,t] & [y,z,t] special
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import Debug.Trace
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import Data.List
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import Prime
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is_couple_prime x y = ( is_prime $ read $ strx ++ stry ) && (is_prime $ read $ stry ++ strx)
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where
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strx = show x
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stry = show y
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first_concat_prime_with_list x [] = True
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first_concat_prime_with_list x (y:ys) = is_couple_prime x y && first_concat_prime_with_list x ys
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-- are_concat_primes [3,7,109,673] return true if number are primes
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-- even with concat
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are_concat_primes [] = True
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are_concat_primes (x:xs) = (are_concat_primes xs) && first_concat_prime_with_list x xs
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special_numbers 1 = take 300 primes
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-- special_numbers n = nub $ flatten $ filter (\x -> traceShow x are_concat_primes x) $ subsets n (special_numbers (n-1))
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special_numbers n = nub $ flatten $ filter are_concat_primes $ subsets n (special_numbers (n-1))
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where
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flatten [] = []
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flatten ([]:ys) = flatten ys
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flatten ((x:xs):ys) = x:flatten (xs:ys)
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subsets :: Integer -> [a] -> [[a]]
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subsets 0 _ = [[]]
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subsets n [] = []
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subsets n (x:xs) = [x:ys | ys <- subsets (n-1) xs ] ++ subsets n xs
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main = do
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putStrLn $ show $ are_concat_primes [3,7,109,673]
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putStrLn $ show $ numbers
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putStrLn $ show $ result
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where
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numbers = take 5 $ special_numbers 5
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result = sum numbers
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