Check a number for Permutable Prime

Given a number N, task is to Check whether it is a permutable prime number or not.

A Permutable prime number is that number which after switching the position of digits through any permutation is also prime. Some of the permutable prime numbers are 2, 3, 5, 7, 11, etc.

Prerequisites : Primality Test | CPP next_permute()



Examples :

Input : 31
Output : Yes
Explanation : 
Both 13 and 31 are prime.

Input : 19
Output : No
Explanation : 
19 is prime but 91 is not

Approach :
1) Construct Sieve of Eratosthenes to find the prime numbers efficiently.
2) Either generate every permutation of the number by switching its digits or use inbuilt C++ function next_permutation to check whether it is prime
3) If any permutation of digits is not prime, simply answer is NO, otherwise YES.

Below is the implementation of above approach.

C++

filter_none

edit
close

play_arrow

link
brightness_4
code

// CPP Program to check whether number is
// permutable prime or not
#include <bits/stdc++.h>
using namespace std;
  
#define MAX 1000001
  
// Sieve of Eratosthenes to find the
// prime numbers upto MAX efficiently
void sieveOfEratosthenes(bool* primes)
{
    // 1 is neither prime nor composite
    primes[1] = false;
  
    for (int i = 2; i * i < MAX; i++) {
  
        // If prime[i] is not changed,
        // then it is a prime
        if (primes[i] == true) {
  
            // Update all multiples of i
            for (int j = i * 2; j < MAX; j += i)
                primes[j] = false;
        }
    }
}
  
// Function returns 1 if the number N is
// permutable prime otherwise not
bool checkPermutablePrime(int N)
{
    // Boolean Array for prime numbers
    bool primes[MAX];
  
    // Initialize all entries as true.
    // A value in prime[i] will finally
    // be false if i is not a prime,
    // else true.
    memset(primes, true, sizeof(primes));
  
    sieveOfEratosthenes(primes);
  
    // Creating Array to store digits
    int num[7];
  
    // Convert the number into array of digits
    int pos = 0;
    while (N > 0) {
        num[pos++] = N % 10;
        N /= 10;
    }
  
    // Size of Array
    int SZ = pos;
    int flag = 0;
  
    sort(num, num + SZ);
  
    do {
  
        // Construct the number again
        // from array of digits
        int temp = 0;
        pos = 0;
        while (pos < SZ) {
            temp = temp * 10 + num[pos];
            pos++;
        }
  
        // check if it is prime of not
        if (primes[temp] == false) {
            flag = 1;
            break;
        }
    } while (next_permutation(num, num + SZ));
  
    // If flag is 1, number
    // is not permutable prime
    if (flag)
        return false;
  
    return true;
}
  
// Driver Code to check above functions
int main()
{
    int N = 31;
    cout << (checkPermutablePrime(N) == 1 ? 
                      "Yes" : "No") << endl;
  
    N = 19;
    cout << (checkPermutablePrime(N) == 1 ? 
                      "Yes" : "No") << endl;
    return 0;
}

chevron_right


PHP

filter_none

edit
close

play_arrow

link
brightness_4
code

<?php
// PHP Program to check 
// whether number is
// permutable prime or not
$MAX = 100001;
$zz;
$l = 0;
  
// to find all permutation
// of that number
function next_permutation($items
                          $perms = array( )) 
{
    global $zz, $l;
    if (empty($items)) 
    
        $zz[$l++] = join($perms);
    
      
    else 
    {
        for ($i = count($items) - 1; 
             $i >= 0; --$i
        {
            $newitems = $items;
            $newperms = $perms;
            list($foo) = array_splice($newitems, $i, 1);
            array_unshift($newperms, $foo);
            next_permutation($newitems, $newperms);
        }
    }
    return $zz;
}
  
// Sieve of Eratosthenes to 
// find the prime numbers 
// upto MAX efficiently
function sieveOfEratosthenes($primes)
{
    global $MAX;
      
    // 1 is neither prime 
    // nor composite
    $primes[1] = false;
  
    for ($i = 2; $i * $i < $MAX; $i++)
    {
  
        // If prime[i] is not changed,
        // then it is a prime
        if ($primes[$i] == true)
        {
  
            // Update all multiples of i
            for ($j = $i * 2; 
                 $j < $MAX; $j += $i)
                $primes[$j] = false;
        }
    }
    return $primes;
}
  
// Function returns 1 if the 
// number N is permutable
// prime otherwise not
function checkPermutablePrime($N)
{
    global $MAX, $zz, $l;
      
    // Boolean Array for
    // prime numbers
  
    // Initialize all entries 
    // as true. A value in 
    // prime[i] will finally
    // be false if i is not a 
    // prime, else true.
    $primes = array_fill(0, $MAX, true);
  
    $primes = sieveOfEratosthenes($primes);
  
    // Creating Array 
    // to store digits
    $num = array();
  
    // Convert the number 
    // into array of digits
    $pos = 0;
    while ($N > 0) 
    {
        $num[$pos++] = $N % 10;
        $N = (int)($N / 10);
    }
  
    // Size of Array
    $flag = 0;
  
    sort($num);
    $num1 = next_permutation($num);
    $i = 0;
    while ($i < count($num1))
    {
  
        // Construct the number again
        // from array of digits
        $temp = 0;
        $pos = 0;
        while ($pos < strlen($num1[$i])) 
        {
            $temp = $temp * 10 + 
                ord($num1[$i][$pos]) - 48;
            $pos++;
        }
  
        // check if it is
        // prime of not
        if ($primes[$temp] == false)
        {
            $flag = 1;
            break;
        }
        $i++;
    }
      
    $zz = array();
    $l = 0;
  
    // If flag is 1, number
    // is not permutable prime
    if ($flag)
        return false;
  
    return true;
}
  
// Driver Code
$N = 31;
echo (checkPermutablePrime($N) == 1 ? 
                              "Yes" : "No") . "\n";
  
$N = 19;
echo (checkPermutablePrime($N) == 1 ? 
                              "Yes" : "No") . "\n";
  
// This Code is contributed
// by mits
?>

chevron_right


Output:

Yes
No


My Personal Notes arrow_drop_up

Check out this Author's contributed articles.

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.



Improved By : Mithun Kumar



Article Tags :
Practice Tags :


Be the First to upvote.


Please write to us at contribute@geeksforgeeks.org to report any issue with the above content.