Primos permutables

PorJosé A. Alonso 11-abril-201618-abril-2016

Un primo permutable es un número primo tal que todos los números obtenidos permutando sus cifras son primos. Por ejemplo, 337 es un primo permutable ya que 337, 373 y 733 son primos.

Definir las funciones

   esPrimoPermutable :: Integer -> Bool
   primosPermutables :: [Integer]

1 2	esPrimoPermutable :: Integer -> Bool primosPermutables :: [Integer]

tales que

(esPrimoPermutable x) se verifica si x es un primo permutable. Por ejemplo,

     esPrimoPermutable 97  ==  True
     esPrimoPermutable 337 ==  True
     esPrimoPermutable 23  ==  False

esPrimoPermutable 97 == True

esPrimoPermutable 337 == True

esPrimoPermutable 23 == False

primosPermutables es la lista de los primos permutables. Por ejemplo,

     λ> take 20 primosPermutables
     [2,3,5,7,11,13,17,31,37,71,73,79,97,113,131,199,311,337,373,733]

1 2	λ> take 20 primosPermutables [2,3,5,7,11,13,17,31,37,71,73,79,97,113,131,199,311,337,373,733]

Soluciones

import Data.List (nub, permutations)
import Data.Numbers.Primes (primes, isPrime)

-- 1ª solución
-- ===========
    
esPrimoPermutable :: Integer -> Bool
esPrimoPermutable x =
    all isPrime (permutacionesN x)

permutacionesN :: Integer -> [Integer]
permutacionesN x =
    [read ys | ys <- nub (permutations xs)]
    where xs = show x
          n  = length xs
        
primosPermutables :: [Integer]
primosPermutables =
    [x | x <- primes, esPrimoPermutable x]

-- 2ª solución
-- ===========

esPrimoPermutable2 :: Integer -> Bool
esPrimoPermutable2 = all isPrime . map read . nub . permutations . show
 
primosPermutables2 :: [Integer]
primosPermutables2 = filter esPrimoPermutable2 primes

import Data.List (nub, permutations)

import Data.Numbers.Primes (primes, isPrime)

-- 1ª solución

-- ===========

esPrimoPermutable :: Integer -> Bool

esPrimoPermutable x =

all isPrime (permutacionesN x)

permutacionesN :: Integer -> [Integer]

permutacionesN x =

[read ys | ys <- nub (permutations xs)]

where xs = show x

n = length xs

primosPermutables :: [Integer]

primosPermutables =

[x | x <- primes, esPrimoPermutable x]

-- 2ª solución

-- ===========

esPrimoPermutable2 :: Integer -> Bool

esPrimoPermutable2 = all isPrime . map read . nub . permutations . show

primosPermutables2 :: [Integer]

primosPermutables2 = filter esPrimoPermutable2 primes

Referencias

Permutable prime en Wikipedia.
Sucesión A003459 de la OEIS.

4 Comentarios

import Data.Numbers.Primes
import Data.List

esPrimoPermutable :: Integer -> Bool
esPrimoPermutable x = and [isPrime ((read z) :: Integer) | z <- permutations (show x)]
                     

primosPermutables :: [Integer]
primosPermutables = [x | x <- primes, esPrimoPermutable x]

import Data.Numbers.Primes

import Data.List

esPrimoPermutable :: Integer -> Bool

esPrimoPermutable x = and [isPrime ((read z) :: Integer) | z <- permutations (show x)]

primosPermutables :: [Integer]

primosPermutables = [x | x <- primes, esPrimoPermutable x]

Responder

import Data.List
import Data.Numbers.Primes

digitos :: Integer->[Integer]
digitos n = [read[c]|c<-show n]

permutaciones:: Show a => a ->[[Char]]
permutaciones n = nub (permutations (show n))

esPrimoPermutable:: Integer->Bool
esPrimoPermutable n = isPrime n && and [isPrime (read c)|c<- permutaciones n]

primoPermutable:: [Integer]
primoPermutable =[x|x<-primes,esPrimoPermutable x]

import Data.List

import Data.Numbers.Primes

digitos :: Integer->[Integer]

digitos n = [read[c]|c<-show n]

permutaciones:: Show a => a ->[[Char]]

permutaciones n = nub (permutations (show n))

esPrimoPermutable:: Integer->Bool

esPrimoPermutable n = isPrime n && and [isPrime (read c)|c<- permutaciones n]

primoPermutable:: [Integer]

primoPermutable =[x|x<-primes,esPrimoPermutable x]

Responder

import Data.Numbers.Primes
import Data.List

esPrimoPermutable :: Integer -> Bool
esPrimoPermutable = all isPrime . map read . permutations . show

primosPermutables :: [Integer]
primosPermutables = filter esPrimoPermutable primes

import Data.Numbers.Primes

import Data.List

esPrimoPermutable :: Integer -> Bool

esPrimoPermutable = all isPrime . map read . permutations . show

primosPermutables :: [Integer]

primosPermutables = filter esPrimoPermutable primes

Responder

import Data.List
import Data.Numbers.Primes

esPrimoPermutable :: Integer -> Bool
esPrimoPermutable 2 = True
esPrimoPermutable n = all odd digs && all isPrime perms
  where digs = [read [i] | i <- show n]
        perms = map (foldr1 toNum) (permutations digs)
        toNum :: Integer -> Integer -> Integer
        toNum x 1 = 10*x+1
        toNum x y = x*10^(ceiling $ logBase 10 (fromIntegral y)) + y 

primosPermutables :: [Integer]
primosPermutables = filter esPrimoPermutable primes

import Data.List

import Data.Numbers.Primes

esPrimoPermutable :: Integer -> Bool

esPrimoPermutable 2 = True

esPrimoPermutable n = all odd digs && all isPrime perms

where digs = [read [i] | i <- show n]

perms = map (foldr1 toNum) (permutations digs)

toNum :: Integer -> Integer -> Integer

toNum x 1 = 10*x+1

toNum x y = x*10^(ceiling $ logBase 10 (fromIntegral y)) + y

primosPermutables :: [Integer]

primosPermutables = filter esPrimoPermutable primes

Responder

Primos permutables

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