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Code Number

Check a number for permutable prime

The given problem is about determining whether a number is a "permutable prime" or not. A permutable prime is a prime number that remains prime when its digits are permuted in any possible order. For example, 37 is a permutable prime because both 37 and 73 are prime numbers.

Problem Statement

The task is to check if a given number is a permutable prime or not. To do this, the code uses a Sieve of Eratosthenes algorithm to generate all prime numbers up to a certain limit and then checks the given number against specific conditions to identify whether it is a permutable prime or not.

Explanation with Example

Let's take the number 37 as an example to illustrate how the code works:

1. First, it will check if the number is greater than 1 and if it is a prime number using the Sieve of Eratosthenes.
2. Since 37 is a prime number, it proceeds to the next step.
3. The code then checks whether the digits of the number are all odd because if there is an even digit (0, 2, 4, 6, or 8), then at least one of its permutations will be divisible by 2 and hence not prime. In this case, 3 and 7 are both odd digits, so it proceeds.
4. It generates all the possible permutations of the digits of 37 (37 and 73) and checks if both of them are prime using the Sieve of Eratosthenes.

Pseudocode

``````procedure swap(digit_num[], i, j)
temp = digit_num[i]
digit_num[i] = digit_num[j]
digit_num[j] = temp

function permutation(collection[], digit_num[], size, n)
if n == size
num = 0
for i = 0 to size
num = num * 10 + digit_num[i]
if collection[num] == 1
return 1
else
return 0
if n < size
for i = n to size
swap(digit_num, i, n)
if not permutation(collection, digit_num, size, n + 1)
return 0
swap(digit_num, i, n)
return 1

function is_permutable_prime(collection[], num)
status = 0
if num > 1 and collection[num] == 1
status = 1
digits = 0
temp = num
while temp != 0
digits++
temp = temp / 10
if digits > 1
create array digit_num[digits]
counter = 0
temp = num
while temp != 0 and status == 1
single_digit = temp % 10
if single_digit is even
status = 0
else
digit_num[counter] = single_digit
temp = temp / 10
counter++
if status == 1
status = permutation(collection, digit_num, digits, 0)
if status == 1
print num, "Is Permutable Prime"
else
print num, "Is Not Permutable Prime"

function sieve_of_eratosthenes(collection[])
i = 0
j = 1
collection[i] = 0
collection[j] = 0
for i = 2 to SIZE
collection[i] = 1
for i = 2 to sqrt(SIZE)
if collection[i] == 1
for j = i * i to SIZE step i
collection[j] = 0

function main()
create array collection[SIZE]
sieve_of_eratosthenes(collection)
is_permutable_prime(collection, 7)
is_permutable_prime(collection, 107)
is_permutable_prime(collection, 13)
is_permutable_prime(collection, 1319)
is_permutable_prime(collection, 1531)
is_permutable_prime(collection, 373)
is_permutable_prime(collection, 991)
``````

Code Solution

Here given code implementation process.

``````// C program
// Check a number for permutable prime
#include <stdio.h>
#define SIZE 1000001

//Swap two elements
void swap(int digit_num[], int i, int j)
{
int temp = digit_num[i];
digit_num[i] = digit_num[j];
digit_num[j] = temp;
}
// Perform permutation of digitsnumber and
// Check whether its is a prime or not
int permutation(int collection[], int digit_num[], int size, int n)
{
if (n == size)
{

int num = 0;
for (int i = 0; i < size; ++i)
{
num = num * 10 + digit_num[i];
}
if (collection[num] == 1)
{
return 1;
}
else
{
return 0;
}
}
if (n < size)
{
for (int i = n; i < size; ++i)
{
//swap the number digit
swap(digit_num, i, n);
if (!permutation(collection, digit_num, size, n + 1))
{
return 0;
}
//swap the number digit
swap(digit_num, i, n);
}
}
return 1;
}
//Check whether given number is permutable prime or not
void is_permutable_prime(int collection[], int num)
{
//indicating the status of result prime number
int status = 0;
//Check that given number is greater than one and number is prime
if (num > 1 && collection[num] == 1)
{
//Active status
status = 1;
int digits = 0;
int temp = num;
//Count the number of digits in given number
while (temp != 0)
{
digits++;
temp /= 10;
}
if (digits > 1)
{
int digit_num[digits];
int counter = 0;
int single_digit = 0;
temp = num;
// Get digits of a number element
// digit sequence is not important
while (temp != 0 && status == 1)
{
single_digit = temp % 10;
if (single_digit % 2 == 0)
{
// When digit is divisible by 2
// that means in permutation last digit is divisible by 2
// [When single digit is 0 2 4 6 8]
status = 0;
}
else
{
digit_num[counter] = single_digit;
temp /= 10;
counter++;
}
}
if (status == 1)
{
//final test
status = permutation(collection, digit_num, digits, 0);
}
}
}
if (status == 1)
{
printf("\n %d Is Permutable Prime", num);
}
else
{
printf("\n %d Is Not Permutable Prime", num);
}
}
//Find all prime numbers under 1000001
void sieve_of_eratosthenes(int collection[])
{
// Loop controlling variables
int i = 0;
int j = 1;
// Initial two numbers are not prime (0 and 1)
collection[i] = 0;
collection[j] = 0;
// Set the initial (2 to n element is prime)
for (i = 2; i < SIZE; ++i)
{
collection[i] = 1;
}
// Initial 0 and 1 are not prime
// We start to 2
for (i = 2; i * i < SIZE; ++i)
{
if (collection[i] == 1)
{
//When i is prime number
//Modify the prime status of all next multiplier of location i
for (j = i * i; j < SIZE; j += i)
{
collection[j] = 0;
}
}
}
}
int main()
{
//This is used to store prime number status
int collection[SIZE];
//Find find prime number
sieve_of_eratosthenes(collection);
//Test case
is_permutable_prime(collection, 7);
is_permutable_prime(collection, 107);
is_permutable_prime(collection, 13);
is_permutable_prime(collection, 1319);
is_permutable_prime(collection, 1531);
is_permutable_prime(collection, 373);
is_permutable_prime(collection, 991);
return 0;
}``````

Output

`````` 7 Is Permutable Prime
107 Is Not Permutable Prime
13 Is Permutable Prime
1319 Is Not Permutable Prime
1531 Is Not Permutable Prime
373 Is Permutable Prime
991 Is Permutable Prime``````
``````// Java porgram
// Check a number for permutable prime
class PermutablePrime
{
//Swap two elements
public void swap(int[] digit_num, int i, int j)
{
int temp = digit_num[i];
digit_num[i] = digit_num[j];
digit_num[j] = temp;
}
// Perform permutation of digitsnumber and
// Check whether its is a prime or not
public boolean permutation(boolean[] collection, int[] digit_num, int size, int n)
{
if (n == size)
{
int num = 0;
for (int i = 0; i < size; ++i)
{
num = num *10 + digit_num[i];
}
if (collection[num] == true)
{
return true;
}
else
{
return false;
}
}
if (n < size)
{
for (int i = n; i < size; ++i)
{
//swap the number digit
swap(digit_num, i, n);
if (!permutation(collection, digit_num, size, n + 1))
{
return false;
}
//swap the number digit
swap(digit_num, i, n);
}
}
return true;
}
//Check whether given number is permutable prime or not
public void is_permutable_prime(boolean[] collection, int num)
{
//indicating the status of result prime number
boolean status = false;
//Check that given number is greater than one and number is prime
if (num > 1 && collection[num] == true)
{
//Active status
status = true;
int digits = 0;
int temp = num;
//Count the number of digits in given number
while (temp != 0)
{
digits++;
temp /= 10;
}
if (digits > 1)
{
int[] digit_num = new int[digits];
int counter = 0;
int single_digit = 0;
temp = num;
// Get digits of a number element
// digit sequence is not important
while (temp != 0 && status == true)
{
single_digit = temp % 10;
if (single_digit % 2 == 0)
{
// When digit is divisible by 2
// that means in permutation last digit is divisible by 2
// [When single digit is 0 2 4 6 8]
status = false;
}
else
{
digit_num[counter] = single_digit;
temp /= 10;
counter++;
}
}
if (status == true)
{
//final test
status = permutation(collection, digit_num, digits, 0);
}
}
}
if (status == true)
{
System.out.print("\n " + num +" Is Permutable Prime");
}
else
{
System.out.print("\n " + num + " Is Not Permutable Prime");
}
}
//Find all prime numbers under 1000001
public void sieve_of_eratosthenes(boolean[] collection, int size)
{
// Loop controlling variables
int i = 0;
int j = 1;
// Initial two numbers are not prime (0 and 1)
collection[i] = false;
collection[j] = false;
// Set the initial (2 to n element is prime)
for (i = 2; i < size; ++i)
{
collection[i] = true;
}
// Initial 0 and 1 are not prime
// We start to 2
for (i = 2; i *i < size; ++i)
{
if (collection[i] == true)
{
//When i is prime number
//Modify the prime status of all next multiplier of location i
for (j = i *i; j < size; j += i)
{
collection[j] = false;
}
}
}
}
public static void main(String args[])
{
PermutablePrime obj = new PermutablePrime();
int size = 1000001;
//This is used to store prime number status
boolean[] collection = new boolean[size];
//Find find prime number
obj.sieve_of_eratosthenes(collection, size);
//Test case
obj.is_permutable_prime(collection, 7);
obj.is_permutable_prime(collection, 107);
obj.is_permutable_prime(collection, 13);
obj.is_permutable_prime(collection, 1319);
obj.is_permutable_prime(collection, 1531);
obj.is_permutable_prime(collection, 373);
obj.is_permutable_prime(collection, 991);
}
}``````

Output

`````` 7 Is Permutable Prime
107 Is Not Permutable Prime
13 Is Permutable Prime
1319 Is Not Permutable Prime
1531 Is Not Permutable Prime
373 Is Permutable Prime
991 Is Permutable Prime``````
``````//Include header file
#include <iostream>
using namespace std;

// C++ porgram
// Check a number for permutable prime
class PermutablePrime
{
public:
//Swap two elements
void swap(int digit_num[], int i, int j)
{
int temp = digit_num[i];
digit_num[i] = digit_num[j];
digit_num[j] = temp;
}
// Perform permutation of digitsnumber and
// Check whether its is a prime or not
bool permutation(bool collection[], int digit_num[], int size, int n)
{
if (n == size)
{
int num = 0;
for (int i = 0; i < size; ++i)
{
num = num *10 + digit_num[i];
}
if (collection[num] == true)
{
return true;
}
else
{
return false;
}
}
if (n < size)
{
for (int i = n; i < size; ++i)
{
//swap the number digit
this->swap(digit_num, i, n);
if (!this->permutation(collection, digit_num, size, n + 1))
{
return false;
}
//swap the number digit
this->swap(digit_num, i, n);
}
}
return true;
}
//Check whether given number is permutable prime or not
void is_permutable_prime(bool collection[], int num)
{
//indicating the status of result prime number
bool status = false;
//Check that given number is greater than one and number is prime
if (num > 1 && collection[num] == true)
{
//Active status
status = true;
int digits = 0;
int temp = num;
//Count the number of digits in given number
while (temp != 0)
{
digits++;
temp /= 10;
}
if (digits > 1)
{
int digit_num[digits] ;
int counter = 0;
int single_digit = 0;
temp = num;
// Get digits of a number element
// digit sequence is not important
while (temp != 0 && status == true)
{
single_digit = temp % 10;
if (single_digit % 2 == 0)
{
// When digit is divisible by 2
// that means in permutation last digit is divisible by 2
// [When single digit is 0 2 4 6 8]
status = false;
}
else
{
digit_num[counter] = single_digit;
temp /= 10;
counter++;
}
}
if (status == true)
{
//final test
status = this->permutation(collection, digit_num, digits, 0);
}
}
}
if (status == true)
{
cout << "\n " << num << " Is Permutable Prime";
}
else
{
cout << "\n " << num << " Is Not Permutable Prime";
}
}
//Find all prime numbers under 1000001
void sieve_of_eratosthenes(bool collection[], int size)
{
// Loop controlling variables
int i = 0;
int j = 1;
// Initial two numbers are not prime (0 and 1)
collection[i] = false;
collection[j] = false;
// Set the initial (2 to n element is prime)
for (i = 2; i < size; ++i)
{
collection[i] = true;
}
// Initial 0 and 1 are not prime
// We start to 2
for (i = 2; i *i < size; ++i)
{
if (collection[i] == true)
{
//When i is prime number
//Modify the prime status of all next multiplier of location i
for (j = i *i; j < size; j += i)
{
collection[j] = false;
}
}
}
}
};
int main()
{
PermutablePrime obj = PermutablePrime();
int size = 1000001;
//This is used to store prime number status
bool collection[size] ;
//Find find prime number
obj.sieve_of_eratosthenes(collection, size);
//Test case
obj.is_permutable_prime(collection, 7);
obj.is_permutable_prime(collection, 107);
obj.is_permutable_prime(collection, 13);
obj.is_permutable_prime(collection, 1319);
obj.is_permutable_prime(collection, 1531);
obj.is_permutable_prime(collection, 373);
obj.is_permutable_prime(collection, 991);
return 0;
}``````

Output

`````` 7 Is Permutable Prime
107 Is Not Permutable Prime
13 Is Permutable Prime
1319 Is Not Permutable Prime
1531 Is Not Permutable Prime
373 Is Permutable Prime
991 Is Permutable Prime``````
``````//Include namespace system
using System;

// C# porgram
// Check a number for permutable prime

class PermutablePrime
{
//Swap two elements
public void swap(int[] digit_num, int i, int j)
{
int temp = digit_num[i];
digit_num[i] = digit_num[j];
digit_num[j] = temp;
}
// Perform permutation of digitsnumber and
// Check whether its is a prime or not
public Boolean permutation(Boolean[] collection, int[] digit_num, int size, int n)
{
if (n == size)
{
int num = 0;
for (int i = 0; i < size; ++i)
{
num = num * 10 + digit_num[i];
}
if (collection[num] == true)
{
return true;
}
else
{
return false;
}
}
if (n < size)
{
for (int i = n; i < size; ++i)
{
//swap the number digit
swap(digit_num, i, n);
if (!permutation(collection, digit_num, size, n + 1))
{
return false;
}
//swap the number digit
swap(digit_num, i, n);
}
}
return true;
}
//Check whether given number is permutable prime or not
public void is_permutable_prime(Boolean[] collection, int num)
{
//indicating the status of result prime number
Boolean status = false;
//Check that given number is greater than one and number is prime
if (num > 1 && collection[num] == true)
{
//Active status
status = true;
int digits = 0;
int temp = num;
//Count the number of digits in given number
while (temp != 0)
{
digits++;
temp /= 10;
}
if (digits > 1)
{
int[] digit_num = new int[digits];
int counter = 0;
int single_digit = 0;
temp = num;
// Get digits of a number element
// digit sequence is not important
while (temp != 0 && status == true)
{
single_digit = temp % 10;
if (single_digit % 2 == 0)
{
// When digit is divisible by 2
// that means in permutation last digit is divisible by 2
// [When single digit is 0 2 4 6 8]
status = false;
}
else
{
digit_num[counter] = single_digit;
temp /= 10;
counter++;
}
}
if (status == true)
{
//final test
status = permutation(collection, digit_num, digits, 0);
}
}
}
if (status == true)
{
Console.Write("\n " + num + " Is Permutable Prime");
}
else
{
Console.Write("\n " + num + " Is Not Permutable Prime");
}
}
//Find all prime numbers under 1000001
public void sieve_of_eratosthenes(Boolean[] collection, int size)
{
// Loop controlling variables
int i = 0;
int j = 1;
// Initial two numbers are not prime (0 and 1)
collection[i] = false;
collection[j] = false;
// Set the initial (2 to n element is prime)
for (i = 2; i < size; ++i)
{
collection[i] = true;
}
// Initial 0 and 1 are not prime
// We start to 2
for (i = 2; i * i < size; ++i)
{
if (collection[i] == true)
{
//When i is prime number
//Modify the prime status of all next multiplier of location i
for (j = i * i; j < size; j += i)
{
collection[j] = false;
}
}
}
}
public static void Main(String []args)
{
PermutablePrime obj = new PermutablePrime();
int size = 1000001;
//This is used to store prime number status
Boolean[] collection = new Boolean[size];
//Find find prime number
obj.sieve_of_eratosthenes(collection, size);
//Test case
obj.is_permutable_prime(collection, 7);
obj.is_permutable_prime(collection, 107);
obj.is_permutable_prime(collection, 13);
obj.is_permutable_prime(collection, 1319);
obj.is_permutable_prime(collection, 1531);
obj.is_permutable_prime(collection, 373);
obj.is_permutable_prime(collection, 991);
}
}``````

Output

`````` 7 Is Permutable Prime
107 Is Not Permutable Prime
13 Is Permutable Prime
1319 Is Not Permutable Prime
1531 Is Not Permutable Prime
373 Is Permutable Prime
991 Is Permutable Prime``````
``````<?php
// Php porgram
// Check a number for permutable prime
class PermutablePrime
{
//Swap two elements
public  function swap( & \$digit_num, \$i, \$j)
{
\$temp = \$digit_num[\$i];
\$digit_num[\$i] = \$digit_num[\$j];
\$digit_num[\$j] = \$temp;
}
// Perform permutation of digitsnumber and
// Check whether its is a prime or not
public  function permutation( & \$collection, & \$digit_num, \$size, \$n)
{
if (\$n == \$size)
{
\$num = 0;
for (\$i = 0; \$i < \$size; ++\$i)
{
\$num = \$num * 10 + \$digit_num[\$i];
}
if (\$collection[\$num] == true)
{
return true;
}
else
{
return false;
}
}
if (\$n < \$size)
{
for (\$i = \$n; \$i < \$size; ++\$i)
{
//swap the number digit
\$this->swap(\$digit_num, \$i, \$n);
if (!\$this->permutation(\$collection, \$digit_num, \$size, \$n + 1))
{
return false;
}
//swap the number digit
\$this->swap(\$digit_num, \$i, \$n);
}
}
return true;
}
//Check whether given number is permutable prime or not
public  function is_permutable_prime( & \$collection, \$num)
{
//indicating the status of result prime number
\$status = false;
//Check that given number is greater than one and number is prime
if (\$num > 1 && \$collection[\$num] == true)
{
//Active status
\$status = true;
\$digits = 0;
\$temp = \$num;
//Count the number of digits in given number
while (\$temp != 0)
{
\$digits++;
\$temp = intval(\$temp / 10);
}
if (\$digits > 1)
{
\$digit_num = array_fill(0, \$digits, 0);
\$counter = 0;
\$single_digit = 0;
\$temp = \$num;
// Get digits of a number element
// digit sequence is not important
while (\$temp != 0 && \$status == true)
{
\$single_digit = \$temp % 10;
if (\$single_digit % 2 == 0)
{
// When digit is divisible by 2
// that means in permutation last digit is divisible by 2
// [When single digit is 0 2 4 6 8]
\$status = false;
}
else
{
\$digit_num[\$counter] = \$single_digit;
\$temp = intval(\$temp / 10);
\$counter++;
}
}
if (\$status == true)
{
//final test
\$status = \$this->permutation(\$collection, \$digit_num, \$digits, 0);
}
}
}
if (\$status == true)
{
echo "\n ". \$num ." Is Permutable Prime";
}
else
{
echo "\n ". \$num ." Is Not Permutable Prime";
}
}
//Find all prime numbers under 1000001
public  function sieve_of_eratosthenes( & \$collection, \$size)
{
// Loop controlling variables
\$i = 0;
\$j = 1;
// Initial two numbers are not prime (0 and 1)
\$collection[\$i] = false;
\$collection[\$j] = false;
// Set the initial (2 to n element is prime)
for (\$i = 2; \$i < \$size; ++\$i)
{
\$collection[\$i] = true;
}
// Initial 0 and 1 are not prime
// We start to 2
for (\$i = 2; \$i * \$i < \$size; ++\$i)
{
if (\$collection[\$i] == true)
{
//When i is prime number
//Modify the prime status of all next multiplier of location i
for (\$j = \$i * \$i; \$j < \$size; \$j += \$i)
{
\$collection[\$j] = false;
}
}
}
}
}

function main()
{
\$obj = new PermutablePrime();
\$size = 1000001;
//This is used to store prime number status
\$collection = array_fill(0, \$size, false);
//Find find prime number
\$obj->sieve_of_eratosthenes(\$collection, \$size);
//Test case
\$obj->is_permutable_prime(\$collection, 7);
\$obj->is_permutable_prime(\$collection, 107);
\$obj->is_permutable_prime(\$collection, 13);
\$obj->is_permutable_prime(\$collection, 1319);
\$obj->is_permutable_prime(\$collection, 1531);
\$obj->is_permutable_prime(\$collection, 373);
\$obj->is_permutable_prime(\$collection, 991);
}
main();``````

Output

`````` 7 Is Permutable Prime
107 Is Not Permutable Prime
13 Is Permutable Prime
1319 Is Not Permutable Prime
1531 Is Not Permutable Prime
373 Is Permutable Prime
991 Is Permutable Prime``````
``````// Node Js porgram
// Check a number for permutable prime
class PermutablePrime
{
//Swap two elements
swap(digit_num, i, j)
{
var temp = digit_num[i];
digit_num[i] = digit_num[j];
digit_num[j] = temp;
}
// Perform permutation of digitsnumber and
// Check whether its is a prime or not
permutation(collection, digit_num, size, n)
{
if (n == size)
{
var num = 0;
for (var i = 0; i < size; ++i)
{
num = num * 10 + digit_num[i];
}
if (collection[num] == true)
{
return true;
}
else
{
return false;
}
}
if (n < size)
{
for (var i = n; i < size; ++i)
{
//swap the number digit
this.swap(digit_num, i, n);
if (!this.permutation(collection, digit_num, size, n + 1))
{
return false;
}
//swap the number digit
this.swap(digit_num, i, n);
}
}
return true;
}
//Check whether given number is permutable prime or not
is_permutable_prime(collection, num)
{
//indicating the status of result prime number
var status = false;
//Check that given number is greater than one and number is prime
if (num > 1 && collection[num] == true)
{
//Active status
status = true;
var digits = 0;
var temp = num;
//Count the number of digits in given number
while (temp != 0)
{
digits++;
temp = parseInt(temp / 10);
}
if (digits > 1)
{
var digit_num = Array(digits).fill(0);
var counter = 0;
var single_digit = 0;
temp = num;
// Get digits of a number element
// digit sequence is not important
while (temp != 0 && status == true)
{
single_digit = temp % 10;
if (single_digit % 2 == 0)
{
// When digit is divisible by 2
// that means in permutation last digit is divisible by 2
// [When single digit is 0 2 4 6 8]
status = false;
}
else
{
digit_num[counter] = single_digit;
temp = parseInt(temp / 10);
counter++;
}
}
if (status == true)
{
//final test
status = this.permutation(collection, digit_num, digits, 0);
}
}
}
if (status == true)
{
process.stdout.write("\n " + num + " Is Permutable Prime");
}
else
{
process.stdout.write("\n " + num + " Is Not Permutable Prime");
}
}
//Find all prime numbers under 1000001
sieve_of_eratosthenes(collection, size)
{
// Loop controlling variables
var i = 0;
var j = 1;
// Initial two numbers are not prime (0 and 1)
collection[i] = false;
collection[j] = false;
// Set the initial (2 to n element is prime)
for (i = 2; i < size; ++i)
{
collection[i] = true;
}
// Initial 0 and 1 are not prime
// We start to 2
for (i = 2; i * i < size; ++i)
{
if (collection[i] == true)
{
//When i is prime number
//Modify the prime status of all next multiplier of location i
for (j = i * i; j < size; j += i)
{
collection[j] = false;
}
}
}
}
}

function main()
{
var obj = new PermutablePrime();
var size = 1000001;
//This is used to store prime number status
var collection = Array(size).fill(false);
//Find find prime number
obj.sieve_of_eratosthenes(collection, size);
//Test case
obj.is_permutable_prime(collection, 7);
obj.is_permutable_prime(collection, 107);
obj.is_permutable_prime(collection, 13);
obj.is_permutable_prime(collection, 1319);
obj.is_permutable_prime(collection, 1531);
obj.is_permutable_prime(collection, 373);
obj.is_permutable_prime(collection, 991);
}
main();``````

Output

`````` 7 Is Permutable Prime
107 Is Not Permutable Prime
13 Is Permutable Prime
1319 Is Not Permutable Prime
1531 Is Not Permutable Prime
373 Is Permutable Prime
991 Is Permutable Prime``````
``````#  Python 3 porgram
#  Check a number for permutable prime
class PermutablePrime :
# Swap two elements
def swap(self, digit_num, i, j) :
temp = digit_num[i]
digit_num[i] = digit_num[j]
digit_num[j] = temp

#  Perform permutation of digitsnumber and
#  Check whether its is a prime or not
def permutation(self, collection, digit_num, size, n) :
if (n == size) :
num = 0
i = 0
while (i < size) :
num = num * 10 + digit_num[i]
i += 1

if (collection[num] == True) :
return True
else :
return False

if (n < size) :
i = n
while (i < size) :
# swap the number digit
self.swap(digit_num, i, n)
if (not self.permutation(collection, digit_num, size, n + 1)) :
return False

# swap the number digit
self.swap(digit_num, i, n)
i += 1

return True

# Check whether given number is permutable prime or not
def is_permutable_prime(self, collection, num) :
# indicating the status of result prime number
status = False
# Check that given number is greater than one and number is prime
if (num > 1 and collection[num] == True) :
# Active status
status = True
digits = 0
temp = num
# Count the number of digits in given number
while (temp != 0) :
digits += 1
temp = int(temp / 10)

if (digits > 1) :
digit_num = [0] * (digits)
counter = 0
single_digit = 0
temp = num
#  Get digits of a number element
#  digit sequence is not important
while (temp != 0 and status == True) :
single_digit = temp % 10
if (single_digit % 2 == 0) :
#  When digit is divisible by 2
#  that means in permutation last digit is divisible by 2
#  [When single digit is 0 2 4 6 8]
status = False
else :
digit_num[counter] = single_digit
temp = int(temp / 10)
counter += 1

if (status == True) :
# final test
status = self.permutation(collection, digit_num, digits, 0)

if (status == True) :
print("\n ", num ," Is Permutable Prime", end = "")
else :
print("\n ", num ," Is Not Permutable Prime", end = "")

# Find all prime numbers under 1000001
def sieve_of_eratosthenes(self, collection, size) :
#  Loop controlling variables
i = 0
j = 1
#  Initial two numbers are not prime (0 and 1)
collection[i] = False
collection[j] = False
#  Initial 0 and 1 are not prime
#  We start to 2
i = 2
while (i * i < size) :
if (collection[i] == True) :
# When i is prime number
# Modify the prime status of all next multiplier of location i
j = i * i
while (j < size) :
collection[j] = False
j += i

i += 1

def main() :
obj = PermutablePrime()
size = 1000001
# This is used to store prime number status
collection = [True] * (size)
# Find find prime number
obj.sieve_of_eratosthenes(collection, size)
# Test case
obj.is_permutable_prime(collection, 7)
obj.is_permutable_prime(collection, 107)
obj.is_permutable_prime(collection, 13)
obj.is_permutable_prime(collection, 1319)
obj.is_permutable_prime(collection, 1531)
obj.is_permutable_prime(collection, 373)
obj.is_permutable_prime(collection, 991)

if __name__ == "__main__": main()``````

Output

``````  7  Is Permutable Prime
107  Is Not Permutable Prime
13  Is Permutable Prime
1319  Is Not Permutable Prime
1531  Is Not Permutable Prime
373  Is Permutable Prime
991  Is Permutable Prime``````
``````#  Ruby porgram
#  Check a number for permutable prime
class PermutablePrime
# Swap two elements
def swap(digit_num, i, j)
temp = digit_num[i]
digit_num[i] = digit_num[j]
digit_num[j] = temp
end

#  Perform permutation of digitsnumber and
#  Check whether its is a prime or not
def permutation(collection, digit_num, size, n)
if (n == size)
num = 0
i = 0
while (i < size)
num = num * 10 + digit_num[i]
i += 1
end

if (collection[num] == true)
return true
else
return false
end

end

if (n < size)
i = n
while (i < size)
# swap the number digit
self.swap(digit_num, i, n)
if (!self.permutation(collection, digit_num, size, n + 1))
return false
end

# swap the number digit
self.swap(digit_num, i, n)
i += 1
end

end

return true
end

# Check whether given number is permutable prime or not
def is_permutable_prime(collection, num)
# indicating the status of result prime number
status = false
# Check that given number is greater than one and number is prime
if (num > 1 && collection[num] == true)
# Active status
status = true
digits = 0
temp = num
# Count the number of digits in given number
while (temp != 0)
digits += 1
temp /= 10
end

if (digits > 1)
digit_num = Array.new(digits) {0}
counter = 0
single_digit = 0
temp = num
#  Get digits of a number element
#  digit sequence is not important
while (temp != 0 && status == true)
single_digit = temp % 10
if (single_digit % 2 == 0)
#  When digit is divisible by 2
#  that means in permutation last digit is divisible by 2
#  [When single digit is 0 2 4 6 8]
status = false
else
digit_num[counter] = single_digit
temp /= 10
counter += 1
end

end

if (status == true)
# final test
status = self.permutation(collection, digit_num, digits, 0)
end

end

end

if (status == true)
print("\n ", num ," Is Permutable Prime")
else
print("\n ", num ," Is Not Permutable Prime")
end

end

# Find all prime numbers under 1000001
def sieve_of_eratosthenes(collection, size)
#  Loop controlling variables
i = 0
j = 1
#  Initial two numbers are not prime (0 and 1)
collection[i] = false
collection[j] = false
#  Initial 0 and 1 are not prime
#  We start to 2
i = 2
while (i * i < size)
if (collection[i] == true)
# When i is prime number
# Modify the prime status of all next multiplier of location i
j = i * i
while (j < size)
collection[j] = false
j += i
end

end

i += 1
end

end

end

def main()
obj = PermutablePrime.new()
size = 1000001
# This is used to store prime number status
collection = Array.new(size) {true}
# Find find prime number
obj.sieve_of_eratosthenes(collection, size)
# Test case
obj.is_permutable_prime(collection, 7)
obj.is_permutable_prime(collection, 107)
obj.is_permutable_prime(collection, 13)
obj.is_permutable_prime(collection, 1319)
obj.is_permutable_prime(collection, 1531)
obj.is_permutable_prime(collection, 373)
obj.is_permutable_prime(collection, 991)
end

main()``````

Output

`````` 7 Is Permutable Prime
107 Is Not Permutable Prime
13 Is Permutable Prime
1319 Is Not Permutable Prime
1531 Is Not Permutable Prime
373 Is Permutable Prime
991 Is Permutable Prime``````
``````// Scala porgram
// Check a number for permutable prime
class PermutablePrime
{
//Swap two elements
def swap(digit_num: Array[Int], i: Int, j: Int): Unit = {
var temp: Int = digit_num(i);
digit_num(i) = digit_num(j);
digit_num(j) = temp;
}
// Perform permutation of digitsnumber and
// Check whether its is a prime or not
def permutation(collection: Array[Boolean], digit_num: Array[Int], size: Int, n: Int): Boolean = {
var i: Int = 0;
if (n == size)
{
var num: Int = 0;
while (i < size)
{
num = num * 10 + digit_num(i);
i += 1;
}
if (collection(num) == true)
{
return true;
}
else
{
return false;
}
}
if (n < size)
{
i = n;
while (i < size)
{
//swap the number digit
swap(digit_num, i, n);
if (!permutation(collection, digit_num, size, n + 1))
{
return false;
}
//swap the number digit
swap(digit_num, i, n);
i += 1;
}
}
return true;
}
//Check whether given number is permutable prime or not
def is_permutable_prime(collection: Array[Boolean], num: Int): Unit = {
//indicating the status of result prime number
var status: Boolean = false;
//Check that given number is greater than one and number is prime
if (num > 1 && collection(num) == true)
{
//Active status
status = true;
var digits: Int = 0;
var temp: Int = num;
//Count the number of digits in given number
while (temp != 0)
{
digits += 1;
temp = (temp / 10).toInt;
}
if (digits > 1)
{
var digit_num: Array[Int] = Array.fill[Int](digits)(0);
var counter: Int = 0;
var single_digit: Int = 0;
temp = num;
// Get digits of a number element
// digit sequence is not important
while (temp != 0 && status == true)
{
single_digit = temp % 10;
if (single_digit % 2 == 0)
{
// When digit is divisible by 2
// that means in permutation last digit is divisible by 2
// [When single digit is 0 2 4 6 8]
status = false;
}
else
{
digit_num(counter) = single_digit;
temp = (temp / 10).toInt;
counter += 1;
}
}
if (status == true)
{
//final test
status = permutation(collection, digit_num, digits, 0);
}
}
}
if (status == true)
{
print("\n " + num + " Is Permutable Prime");
}
else
{
print("\n " + num + " Is Not Permutable Prime");
}
}
//Find all prime numbers under 1000001
def sieve_of_eratosthenes(collection: Array[Boolean], size: Int): Unit = {
// Loop controlling variables
var i: Int = 0;
var j: Int = 1;
// Initial two numbers are not prime (0 and 1)
collection(i) = false;
collection(j) = false;
// Initial 0 and 1 are not prime
// We start to 2
i = 2;
while (i * i < size)
{
if (collection(i) == true)
{
//When i is prime number
//Modify the prime status of all next multiplier of location i
j = i * i;
while (j < size)
{
collection(j) = false;
j += i;
}
}
i += 1;
}
}
}
object Main
{
def main(args: Array[String]): Unit = {
var obj: PermutablePrime = new PermutablePrime();
var size: Int = 1000001;
//This is used to store prime number status
var collection: Array[Boolean] = Array.fill[Boolean](size)(true);
//Find find prime number
obj.sieve_of_eratosthenes(collection, size);
//Test case
obj.is_permutable_prime(collection, 7);
obj.is_permutable_prime(collection, 107);
obj.is_permutable_prime(collection, 13);
obj.is_permutable_prime(collection, 1319);
obj.is_permutable_prime(collection, 1531);
obj.is_permutable_prime(collection, 373);
obj.is_permutable_prime(collection, 991);
}
}``````

Output

`````` 7 Is Permutable Prime
107 Is Not Permutable Prime
13 Is Permutable Prime
1319 Is Not Permutable Prime
1531 Is Not Permutable Prime
373 Is Permutable Prime
991 Is Permutable Prime``````
``````// Swift 4 porgram
// Check a number for permutable prime
class PermutablePrime
{
//Swap two elements
func swap(_ digit_num: inout[Int], _ i: Int, _ j: Int)
{
let temp: Int = digit_num[i];
digit_num[i] = digit_num[j];
digit_num[j] = temp;
}
// Perform permutation of digitsnumber and
// Check whether its is a prime or not
func permutation(_ collection: [Bool], _ digit_num: inout[Int], _ size: Int, _ n: Int) -> Bool
{
var i: Int = 0;
if (n == size)
{
var num: Int = 0;

while (i < size)
{
num = num * 10 + digit_num[i];
i += 1;
}
if (collection[num] == true)
{
return true;
}
else
{
return false;
}
}
if (n < size)
{
i = n;
while (i < size)
{
//swap the number digit
self.swap(&digit_num, i, n);
if (!self.permutation(collection, &digit_num, size, n + 1))
{
return false;
}
//swap the number digit
self.swap(&digit_num, i, n);
i += 1;
}
}
return true;
}
//Check whether given number is permutable prime or not
func is_permutable_prime(_ collection: [Bool], _ num: Int)
{
//indicating the status of result prime number
var status: Bool = false;
//Check that given number is greater than one and number is prime
if (num > 1 && collection[num] == true)
{
//Active status
status = true;
var digits: Int = 0;
var temp: Int = num;
//Count the number of digits in given number
while (temp != 0)
{
digits += 1;
temp /= 10;
}
if (digits > 1)
{
var digit_num: [Int] = Array(repeating: 0, count: digits);
var counter: Int = 0;
var single_digit: Int = 0;
temp = num;
// Get digits of a number element
// digit sequence is not important
while (temp != 0 && status == true)
{

single_digit = temp % 10;
if (single_digit % 2 == 0)
{
// When digit is divisible by 2
// that means in permutation last digit is divisible by 2
// [When single digit is 0 2 4 6 8]
status = false;
}
else
{
digit_num[counter] = single_digit;
temp /= 10;
counter += 1;
}
}
if (status == true)
{
//final test
status = self.permutation(collection, &digit_num, digits, 0);
}
}
}
if (status == true)
{
print("\n ", num ," Is Permutable Prime", terminator: "");
}
else
{
print("\n ", num ," Is Not Permutable Prime", terminator: "");
}
}
//Find all prime numbers under 1000001
func sieve_of_eratosthenes(_ collection: inout[Bool], _ size: Int)
{
// Loop controlling variables
var i: Int = 0;
var j: Int = 1;
// Initial two numbers are not prime (0 and 1)
collection[i] = false;
collection[j] = false;
// Initial 0 and 1 are not prime
// We start to 2
i = 2;
while (i * i < size)
{
if (collection[i] == true)
{
//When i is prime number
//Modify the prime status of all next multiplier of location i
j = i * i;
while (j < size)
{
collection[j] = false;
j += i;
}
}
i += 1;
}

}
}
func main()
{
let obj: PermutablePrime = PermutablePrime();
let size: Int = 1000001;
//This is used to store prime number status
var collection: [Bool] = Array(repeating: true, count: size);
//Find find prime number
obj.sieve_of_eratosthenes(&collection, size);
//Test case
obj.is_permutable_prime(collection, 7);
obj.is_permutable_prime(collection, 107);
obj.is_permutable_prime(collection, 13);
obj.is_permutable_prime(collection, 1319);
obj.is_permutable_prime(collection, 1531);
obj.is_permutable_prime(collection, 373);
obj.is_permutable_prime(collection, 991);
}
main();``````

Output

``````  7  Is Permutable Prime
107  Is Not Permutable Prime
13  Is Permutable Prime
1319  Is Not Permutable Prime
1531  Is Not Permutable Prime
373  Is Permutable Prime
991  Is Permutable Prime``````

Time Complexity

1. Generating all prime numbers using the Sieve of Eratosthenes has a time complexity of O(N log log N), where N is the input size (in this case, N = 1000001).
2. Checking each number for being a permutable prime involves permuting its digits and checking each permutation for primality. Generating all permutations of the digits of an N-digit number takes O(N!) time, but in practice, the number of digits is usually small, so the permutation function can be considered to run in constant time for practical purposes.

Therefore, the overall time complexity of the code is dominated by the Sieve of Eratosthenes, which is O(N log log N).

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