Primos de Kamenetsky

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1. Haskell

   import Data.Numbers.Primes primosKamenetsky :: [Integer] primosKamenetsky = filter esPK primes where esCompuesto = not . isPrime antepuestos n = map (read.(:show n)) ['1'..'9'] esPK n = and (map esCompuesto (antepuestos n))

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   import Data.Numbers.Primes   primosKamenetsky :: [Integer] primosKamenetsky = filter esPK primes   where     esCompuesto = not . isPrime     antepuestos n = map (read.(:show n)) ['1'..'9']     esPK n = and (map esCompuesto (antepuestos n))

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   1. Simplificando un poco:

      Haskell

      import Data.Numbers.Primes primosKamenetsky :: [Integer] primosKamenetsky = filter esPK primes where esCompuesto = not . isPrime antepuestos n = [read (c:show n) | c <- ['1'..'9']] esPK = and . map esCompuesto . antepuestos

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      import Data.Numbers.Primes primosKamenetsky :: [Integer] primosKamenetsky = filter esPK primes   where     esCompuesto = not . isPrime     antepuestos n = [read (c:show n) | c <- ['1'..'9']]     esPK = and . map esCompuesto . antepuestos

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2. Haskell

   import Data.Numbers.Primes primoKamenetsky :: Integer -> Bool primoKamenetsky n | not (isPrime n) = False | otherwise = and [not (isPrime (read (a : show n) :: Integer)) | a <- ['1'..'9']] primosKamenetsky :: [Integer] primosKamenetsky = [ a | a <- [0..] , primoKamenetsky a]

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   import Data.Numbers.Primes   primoKamenetsky :: Integer -> Bool primoKamenetsky n | not (isPrime n) = False                   | otherwise       =                  and [not (isPrime (read (a : show n) :: Integer)) | a <- ['1'..'9']]     primosKamenetsky :: [Integer] primosKamenetsky = [ a | a <- [0..]                        , primoKamenetsky a]

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   1. Corregida

      Haskell

      import Data.Numbers.Primes primoKamenetsky :: Integer -> Bool primoKamenetsky n | not (isPrime n) = False | otherwise = and [not (isPrime (read (a : show n))) | a <- ['1'..'9']] primosKamenetsky :: [Integer] primosKamenetsky = [ a | a <- primes , primoKamenetsky a]

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      import Data.Numbers.Primes   primoKamenetsky :: Integer -> Bool primoKamenetsky n   | not (isPrime n) = False   | otherwise       = and [not (isPrime (read (a : show n))) | a <- ['1'..'9']]    primosKamenetsky :: [Integer] primosKamenetsky = [ a | a <- primes                        , primoKamenetsky a]

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3. Haskell

   import Data.Numbers.Primes (primes) import Math.NumberTheory.Logarithms (integerLog10) import Data.List (groupBy) import Data.Function (on) import Data.Set (fromList, member) kamenetsky :: [ℤ] kamenetsky = g 10 $ groupBy ((≡) `on` integerLog10) primes where g p (xs:ys:zss) = [x | let ms = fromList ((`mod` p) ↥ ys), x ← xs, ¬(x `member` ms)] ⧺ g (10×p) (ys:zss) {- > kamenetsky !! 10000 707563 (6.49 secs, 5,177,852,696 bytes) -}

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   import Data.Numbers.Primes          (primes) import Math.NumberTheory.Logarithms (integerLog10) import Data.List                    (groupBy) import Data.Function                (on) import Data.Set                     (fromList, member)   kamenetsky :: [ℤ] kamenetsky = g 10 $ groupBy ((≡) `on` integerLog10) primes   where g p (xs:ys:zss) = [x | let ms = fromList ((`mod` p) ↥ ys), x ← xs, ¬(x `member` ms)]                         ⧺ g (10×p) (ys:zss)                                                   {-   > kamenetsky !! 10000 707563 (6.49 secs, 5,177,852,696 bytes)   -}

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4. Haskell

   import Data.Numbers.Primes primosKamenetsky :: [Integer] primosKamenetsky = [x | x <- primes, isKamenetsky x] where isKamenetsky :: Integer -> Bool isKamenetsky n = not (any (isPrime) [(read (x:(show n)))::Integer | x <- ['1'..'9']])

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   import Data.Numbers.Primes   primosKamenetsky :: [Integer] primosKamenetsky = [x | x <- primes, isKamenetsky x] where isKamenetsky :: Integer -> Bool        isKamenetsky n = not (any (isPrime) [(read (x:(show n)))::Integer | x <- ['1'..'9']])

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5. Haskell

   factores n = [x | x <- [1..n], mod n x == 0] primo n = factores n == [1,n] anadirCifra :: Integer -> [Integer] anadirCifra n = map read [x : show n | x <- ['1'..'9']] prop :: [Integer] -> Bool prop [] = True prop (x:xs) = not (primo x) && prop xs esNK :: Integer -> Bool esNK n = primo n && prop (anadirCifra n) primosKamenetsky :: [Integer] primosKamenetsky = [n | n <- [1..], esNK n] -- λ> take 7 primosKamenetsky -- (0.66 secs, 116,173,224 bytes)

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   factores n = [x | x <- [1..n], mod n x == 0] primo    n = factores n == [1,n]   anadirCifra :: Integer -> [Integer] anadirCifra n = map read [x : show n | x <- ['1'..'9']]   prop :: [Integer] -> Bool prop [] = True prop (x:xs) = not (primo x) && prop xs   esNK :: Integer -> Bool esNK n = primo n && prop (anadirCifra n)   primosKamenetsky :: [Integer] primosKamenetsky = [n | n <- [1..], esNK n]     -- λ> take 7 primosKamenetsky -- (0.66 secs, 116,173,224 bytes)

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6. Haskell

   import Data.Numbers.Primes import Data.List primosKamenetsky :: [Integer] primosKamenetsky = [x | x <- primes, esPrimoKamenetsky x == True] esPrimoKamenetsky :: Integer -> Bool esPrimoKamenetsky a | isPrime a == True && (all esCompuesto (map listaNumeroR (unirDigito (digitosC a)))) == True = True | otherwise = False esCompuesto :: Integer -> Bool esCompuesto a = factores a /= [1,a] && factores a /= [1] factores :: Integer -> [Integer] factores n = [x | x <- [1..n], n `mod` x == 0] digitosC :: Integer -> [Integer] digitosC n = [read [x] | x <- show n] listaNumeroR :: [Integer] -> Integer listaNumeroR [] = 0 listaNumeroR (x:xs) = x*10^((length xs)) + listaNumeroR xs unirDigito :: [Integer] -> [[Integer]] unirDigito xs = [[x] ++ xs | x <- [1..9]]

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   import Data.Numbers.Primes import Data.List   primosKamenetsky :: [Integer] primosKamenetsky = [x | x <- primes, esPrimoKamenetsky x == True]   esPrimoKamenetsky :: Integer -> Bool esPrimoKamenetsky a   | isPrime a == True &&     (all esCompuesto (map listaNumeroR (unirDigito (digitosC a)))) == True = True    | otherwise = False   esCompuesto :: Integer -> Bool esCompuesto a = factores a /= [1,a] && factores a /= [1]   factores :: Integer -> [Integer] factores n = [x | x <- [1..n], n `mod` x == 0]   digitosC :: Integer -> [Integer] digitosC n = [read [x] | x <- show n]   listaNumeroR :: [Integer] -> Integer listaNumeroR []     = 0 listaNumeroR (x:xs) = x*10^((length xs)) + listaNumeroR xs   unirDigito :: [Integer] -> [[Integer]] unirDigito xs = [[x] ++ xs | x <- [1..9]]

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