# 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
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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++

 `// CPP Program to check whether number is ` `// permutable prime or not ` `#include ` `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 = ``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; ` ` `  `    ``// 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; ` `} `

## PHP

 `= 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`` = 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 ` `?> `

Output:

```Yes
No
```

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