77 lines
2.6 KiB
Haskell
77 lines
2.6 KiB
Haskell
|
--
|
||
|
|
-- The primes 3, 7, 109, and 673, are quite remarkable.
|
||
|
|
-- By taking any two primes and concatenating them in any order the result will always be prime.
|
||
|
|
-- For example, taking 7 and 109, both 7109 and 1097 are prime.
|
||
|
|
-- The sum of these four primes, 792, represents the lowest sum for a set of four primes with this property.
|
||
|
|
--
|
||
|
|
-- Find the lowest sum for a set of five primes for which any two primes concatenate to produce another prime.
|
||
|
|
--
|
||
|
|
|
||
|
|
-- Should use the following property
|
||
|
|
-- [x,y,z,t] special <=> [x,y,z] & [x,y,t] & [x,z,t] & [y,z,t] special
|
||
|
|
|
||
|
|
|
||
|
|
import Debug.Trace
|
||
|
|
import Data.List
|
||
|
|
import Prime
|
||
|
|
|
||
|
|
is_couple_prime x y = ( is_prime $ read $ strx ++ stry ) && (is_prime $ read $ stry ++ strx)
|
||
|
|
where
|
||
|
|
strx = show x
|
||
|
|
stry = show y
|
||
|
|
|
||
|
|
first_concat_prime_with_list x [] = True
|
||
|
|
first_concat_prime_with_list x (y:ys) = is_couple_prime x y && first_concat_prime_with_list x ys
|
||
|
|
|
||
|
|
-- are_concat_primes [3,7,109,673] return true if number are primes
|
||
|
|
-- even with concat
|
||
|
|
are_concat_primes [] = True
|
||
|
|
are_concat_primes (x:xs) = (are_concat_primes xs) && first_concat_prime_with_list x xs
|
||
|
|
|
||
|
|
nb_elements=4
|
||
|
|
|
||
|
|
-- n=5 max=5 -> 12345
|
||
|
|
-- n=5 max=6 -> 12346, 12356, 12456, 13456, 23456
|
||
|
|
-- n=5 max=7 -> 12347, 12357, 12367, 12457, 12467...
|
||
|
|
|
||
|
|
-- n=1 max=1 -> 1
|
||
|
|
-- n=1 max=2 -> 2
|
||
|
|
-- n=1 max=3 -> 3
|
||
|
|
--
|
||
|
|
-- n=2 max=2 -> 12
|
||
|
|
-- n=2 max=3 -> 13, 23
|
||
|
|
-- n=2 max=4 -> 14, 24, 34
|
||
|
|
-- n=2 max=5 -> 15, 26, 35, 45
|
||
|
|
--
|
||
|
|
-- n=3 max=3 -> 123
|
||
|
|
-- n=3 max=4 -> 124, 134, 234
|
||
|
|
-- n=3 max=5 -> 125, 135, 235, 145, 245, 345 (n=2,max=2 ; n=2,max=3 ; n=2,max=4)++[5]
|
||
|
|
|
||
|
|
combination :: (Ord a) => Int -> a -> [a] -> [[a]]
|
||
|
|
combination 0 max list = []
|
||
|
|
combination n max (x:xs@(y:ys))
|
||
|
|
| x>max = []
|
||
|
|
| n==1 &&
|
||
|
|
x<=max && y>max = [[x]]
|
||
|
|
| otherwise = ( map (\z -> x:z) $ combination (n-1) max xs )
|
||
|
|
++ combination n max xs
|
||
|
|
|
||
|
|
all_combinations n xs = foldr (++) [] $ map (\i -> traceShow i combination n (xs!!i) xs) [(n-1)..]
|
||
|
|
|
||
|
|
special_numbers 1 = primes
|
||
|
|
special_numbers n = nub $ flatten $ filter are_concat_primes $ all_combinations n $ special_numbers (n-1)
|
||
|
|
where
|
||
|
|
flatten [] = []
|
||
|
|
flatten ([]:ys) = flatten ys
|
||
|
|
flatten ((x:xs):ys) = x:(flatten ((xs):ys) )
|
||
|
|
|
||
|
|
main = do
|
||
|
|
-- putStrLn $ show $ are_concat_primes [3,7,109,673]
|
||
|
|
-- putStrLn $ show $ are_concat_primes [3,7,19,673]
|
||
|
|
-- putStrLn $ show $ combination 5 5 [1..]
|
||
|
|
-- putStrLn $ show $ take 40 $ all_combinations 5 primes
|
||
|
|
putStrLn $ show $ result
|
||
|
|
-- putStrLn ( "sum: " ++ (show $ sum result))
|
||
|
|
where
|
||
|
|
result = take 1 $ filter (\x -> traceShow x are_concat_primes [3,7,109,673,x]) primes
|