Palindromic Primes - GeeksforGeeks

A palindromic prime (sometimes called a palprime) is a prime number that is also a palindromic number.

Given a number n, print all palindromic primes smaller than or equal to n. For example, If n is 10, the output should be “2, 3, 5, 7′. And if n is 20, the output should be “2, 3, 5, 7, 11′.

Idea is to generate all prime numbers smaller than or equal to given number n and checking every prime number whether it is palindromic or not.

Methods used

To find if a given number is prime or not- sieve-of-eratosthenes method
To check whether the given number is palindromic number or not: Recursive function for checking palindrome

Below is the implementation of above algorithm:

C++

// C++ Program to print all palindromic primes 
// smaller than or equal to n. 
#include<bits/stdc++.h> 
using namespace std; 
  
// A function that reurns true only if num 
// contains one digit 
int oneDigit(int num) 
{ 
    // comparison operation is faster than 
    // division operation. So using following 
    // instead of "return num / 10 == 0;" 
    return (num >= 0 && num < 10); 
} 
  
// A recursive function to find out whether 
// num is palindrome or not. Initially, dupNum 
// contains address of a copy of num. 
bool isPalUtil(int num, int* dupNum) 
{ 
    // Base case (needed for recursion termination): 
    // This statement/ mainly compares the first 
    // digit with the last digit 
    if (oneDigit(num)) 
        return (num == (*dupNum) % 10); 
  
    // This is the key line in this method. Note 
    // that all recursive/ calls have a separate 
    // copy of num, but they all share same copy 
    // of *dupNum. We divide num while moving up 
    // the recursion tree 
    if (!isPalUtil(num/10, dupNum)) 
        return false; 
  
    // The following statements are executed when 
    // we move up the recursion call tree 
    *dupNum /= 10; 
  
    // At this point, if num%10 contains i'th 
    // digit from beiginning, then (*dupNum)%10 
    // contains i'th digit from end 
    return (num % 10 == (*dupNum) % 10); 
} 
  
// The main function that uses recursive function 
// isPalUtil() to find out whether num is palindrome 
// or not 
int isPal(int num) 
{ 
    // If num is negative, make it positive 
    if (num < 0) 
       num = -num; 
  
    // Create a separate copy of num, so that 
    // modifications made to address dupNum don't 
    // change the input number. 
    int *dupNum = new int(num); // *dupNum = num 
  
    return isPalUtil(num, dupNum); 
} 
  
// Function to generate all primes and checking 
// whether number is palindromic or not 
void printPalPrimesLessThanN(int n) 
{ 
    // Create a boolean array "prime[0..n]" and 
    // initialize all entries it as true. A value 
    // in prime[i] will finally be false if i is 
    // Not a prime, else true. 
    bool prime[n+1]; 
    memset(prime, true, sizeof(prime)); 
  
    for (int p=2; p*p<=n; p++) 
    { 
        // If prime[p] is not changed, then it is 
        // a prime 
        if (prime[p] == true) 
        { 
            // Update all multiples of p 
            for (int i=p*2; i<=n; i += p) 
                prime[i] = false; 
        } 
    } 
  
    // Print all palindromic prime numbers 
    for (int p=2; p<=n; p++) 
  
       // checking whether the given number is 
       // prime palindromic or not 
       if (prime[p] && isPal(p)) 
          cout << p << " "; 
} 
  
// Driver Program 
int main() 
{ 
    int n = 100; 
    printf("Palindromic primes smaller than or "
           "equal to %d are :\n", n); 
    printPalPrimesLessThanN(n); 
} 

Java

// Java Program to print all palindromic primes 
// smaller than or equal to n. 
import java.util.*; 
  
class GFG { 
      
    // A function that reurns true only if num 
    // contains one digit 
    static boolean oneDigit(int num) 
    { 
        // comparison operation is faster than 
        // division operation. So using following 
        // instead of "return num / 10 == 0;" 
        return (num >= 0 && num < 10); 
    } 
       
    // A recursive function to find out whether 
    // num is palindrome or not. Initially, dupNum 
    // contains address of a copy of num. 
    static boolean isPalUtil(int num, int dupNum) 
    { 
        // Base case (needed for recursion termination): 
        // This statement/ mainly compares the first 
        // digit with the last digit 
        if (oneDigit(num)) 
            return (num == (dupNum) % 10); 
       
        // This is the key line in this method. Note 
        // that all recursive/ calls have a separate 
        // copy of num, but they all share same copy 
        // of dupNum. We divide num while moving up 
        // the recursion tree 
        if (!isPalUtil(num/10, dupNum)) 
            return false; 
       
        // The following statements are executed when 
        // we move up the recursion call tree 
        dupNum /= 10; 
       
        // At this point, if num%10 contains ith 
        // digit from beginning, then (dupNum)%10 
        // contains ith digit from end 
        return (num % 10 == (dupNum) % 10); 
    } 
       
    // The main function that uses recursive function 
    // isPalUtil() to find out whether num is palindrome 
    // or not 
    static boolean isPal(int num) 
    { 
        // If num is negative, make it positive 
        if (num < 0) 
           num = -num; 
       
        // Create a separate copy of num, so that 
        // modifications made to address dupNum don't 
        // change the input number. 
        int dupNum = num; // dupNum = num 
       
        return isPalUtil(num, dupNum); 
    } 
       
    // Function to generate all primes and checking 
    // whether number is palindromic or not 
    static void printPalPrimesLessThanN(int n) 
    { 
        // Create a boolean array "prime[0..n]" and 
        // initialize all entries it as true. A value 
        // in prime[i] will finally be false if i is 
        // Not a prime, else true. 
        boolean prime[] = new boolean[n+1]; 
       
        Arrays.fill(prime, true); 
          
        for (int p = 2; p*p <= n; p++) 
        { 
            // If prime[p] is not changed, then it is 
            // a prime 
            if (prime[p]) 
            { 
                // Update all multiples of p 
                for (int i = p*2; i <= n; i += p){ 
                    prime[i] = false;} 
            } 
        } 
       
        // Print all palindromic prime numbers 
        for (int p = 2; p <= n; p++){ 
       
           // checking whether the given number is 
           // prime palindromic or not 
           if (prime[p] && isPal(p)){ 
              System.out.print(p + " "); 
              } 
           } 
    } 
      
    // Driver function 
    public static void main(String[] args)  
    { 
         int n = 100; 
            System.out.printf("Palindromic primes smaller than or "
                   +"equal to %d are :\n", n); 
            printPalPrimesLessThanN(n); 
        } 
    } 
          
// This code is contributed by Arnav Kr. Mandal. 

Python3

# Python3 Program to print all palindromic  
# primes smaller than or equal to n.  
      
# A function that reurns true only if  
# num contains one digit  
def oneDigit(num): 
      
    # comparison operation is faster than 
    # division operation. So using following 
    # instead of "return num / 10 == 0;" 
    return (num >= 0 and num < 10);  
      
# A recursive function to find out whether  
# num is palindrome or not. Initially, dupNum  
# contains address of a copy of num. 
def isPalUtil(num, dupNum): 
      
    # Base case (needed for recursion termination):  
    # This statement/ mainly compares the first  
    # digit with the last digit  
    if (oneDigit(num)):  
        return (num == (dupNum) % 10);  
      
    # This is the key line in this method. Note  
    # that all recursive/ calls have a separate  
    # copy of num, but they all share same copy  
    # of dupNum. We divide num while moving up  
    # the recursion tree  
    if (not isPalUtil(int(num / 10), dupNum)):  
        return False;  
      
    # The following statements are executed  
    # when we move up the recursion call tree  
    dupNum =int(dupNum/10);  
      
    # At this point, if num%10 contains ith  
    # digit from beginning, then (dupNum)%10  
    # contains ith digit from end  
    return (num % 10 == (dupNum) % 10);  
      
# The main function that uses recursive  
# function isPalUtil() to find out whether  
# num is palindrome or not  
def isPal(num): 
      
    # If num is negative, make it positive  
    if (num < 0):  
        num = -num;  
      
    # Create a separate copy of num, so that  
    # modifications made to address dupNum  
    # don't change the input number.  
    dupNum = num; # dupNum = num  
      
    return isPalUtil(num, dupNum);  
      
# Function to generate all primes and checking  
# whether number is palindromic or not  
def printPalPrimesLessThanN(n): 
      
    # Create a boolean array "prime[0..n]" and  
    # initialize all entries it as true. A value  
    # in prime[i] will finally be false if i is  
    # Not a prime, else true.  
    prime = [True] * (n + 1);  
    p = 2; 
    while (p * p <= n): 
          
        # If prime[p] is not changed,  
        # then it is a prime  
        if (prime[p]):  
              
            # Update all multiples of p  
            for i in range(p * 2, n + 1, p):  
                prime[i] = False; 
        p += 1; 
          
    # Print all palindromic prime numbers  
    for p in range(2, n + 1):  
          
        # checking whether the given number  
        # is prime palindromic or not  
        if (prime[p] and isPal(p)):  
            print(p, end = " ");  
      
# Driver Code  
n = 100;  
print("Palindromic primes smaller",  
      "than or equal to", n, "are :");  
printPalPrimesLessThanN(n);  
  
# This code is contributed by chandan_jnu 

C#

// C# Program to print all palindromic  
// primes smaller than or equal to n. 
using System;  
  
class GFG { 
      
    // A function that reurns true only 
    // if num contains one digit 
    static bool oneDigit(int num) 
    { 
        // comparison operation is faster than 
        // division operation. So using following 
        // instead of "return num / 10 == 0;" 
        return (num >= 0 && num < 10); 
    } 
      
    // A recursive function to find out whether 
    // num is palindrome or not. Initially, dupNum 
    // contains address of a copy of num. 
    static bool isPalUtil(int num, int dupNum) 
    { 
        // Base case (needed for recursion termination): 
        // This statement/ mainly compares the first 
        // digit with the last digit 
        if (oneDigit(num)) 
            return (num == (dupNum) % 10); 
      
        // This is the key line in this method. Note 
        // that all recursive/ calls have a separate 
        // copy of num, but they all share same copy 
        // of dupNum. We divide num while moving up 
        // the recursion tree 
        if (!isPalUtil(num/10, dupNum)) 
            return false; 
      
        // The following statements are executed when 
        // we move up the recursion call tree 
        dupNum /= 10; 
      
        // At this point, if num%10 contains ith 
        // digit from beginning, then (dupNum)%10 
        // contains ith digit from end 
        return (num % 10 == (dupNum) % 10); 
    } 
      
    // The main function that uses recursive  
    // function isPalUtil() to find out  
    // whether num is palindrome or not 
    static bool isPal(int num) 
    { 
        // If num is negative, make it positive 
        if (num < 0) 
        num = -num; 
      
        // Create a separate copy of num, so that 
        // modifications made to address dupNum don't 
        // change the input number. 
        int dupNum = num; // dupNum = num 
      
        return isPalUtil(num, dupNum); 
    } 
      
    // Function to generate all primes and checking 
    // whether number is palindromic or not 
    static void printPalPrimesLessThanN(int n) 
    { 
        // Create a boolean array "prime[0..n]" and 
        // initialize all entries it as true. A value 
        // in prime[i] will finally be false if i is 
        // Not a prime, else true. 
        bool []prime = new bool[n+1]; 
          
    for (int i=0;i<n+1;i++) 
    prime[i]=true; 
          
        for (int p = 2; p*p <= n; p++) 
        { 
            // If prime[p] is not changed, 
            // then it is a prime 
            if (prime[p]) 
            { 
                // Update all multiples of p 
                for (int i = p*2; i <= n; i += p){ 
                    prime[i] = false;} 
            } 
        } 
      
        // Print all palindromic prime numbers 
        for (int p = 2; p <= n; p++){ 
      
        // checking whether the given number is 
        // prime palindromic or not 
        if (prime[p] && isPal(p)){ 
            Console.Write(p + " "); 
            } 
        } 
    } 
      
    // Driver function 
    public static void Main()  
    { 
        int n = 100; 
        Console.Write("Palindromic primes smaller than or " +  
                      "equal to are :\n", n); 
        printPalPrimesLessThanN(n); 
    } 
} 
          
// This code is contributed by nitin mittal. 

PHP

<?php 
// PHP Program to print all palindromic  
// primes smaller than or equal to n.  
      
// A function that reurns true only  
// if num contains one digit  
function oneDigit($num)  
{  
    // comparison operation is faster than  
    // division operation. So using following  
    // instead of "return num / 10 == 0;"  
    return ($num >= 0 && $num < 10);  
}  
  
// A recursive function to find out whether  
// num is palindrome or not. Initially,  
// dupNum contains address of a copy of num.  
function isPalUtil($num, $dupNum)  
{  
    // Base case (needed for recursion termination):  
    // This statement/ mainly compares the first  
    // digit with the last digit  
    if (oneDigit($num))  
        return ($num == ($dupNum) % 10);  
  
    // This is the key line in this method. Note  
    // that all recursive/ calls have a separate  
    // copy of num, but they all share same copy  
    // of dupNum. We divide num while moving up  
    // the recursion tree  
    if (!isPalUtil((int)($num/10), $dupNum))  
        return false;  
  
    // The following statements are executed   
    // when we move up the recursion call tree  
    $dupNum = (int)($dupNum / 10);  
  
    // At this point, if num%10 contains ith  
    // digit from beginning, then (dupNum)%10  
    // contains ith digit from end  
    return ($num % 10 == ($dupNum) % 10);  
}  
  
// The main function that uses recursive  
// function isPalUtil() to find out whether 
// num is palindrome or not  
function isPal($num)  
{  
    // If num is negative, make it positive  
    if ($num < 0)  
    $num = -$num;  
  
    // Create a separate copy of num, so that  
    // modifications made to address dupNum  
    // don't change the input number.  
    $dupNum = $num; // dupNum = num  
  
    return isPalUtil($num, $dupNum);  
}  
  
// Function to generate all primes and checking  
// whether number is palindromic or not  
function printPalPrimesLessThanN($n)  
{  
    // Create a boolean array "prime[0..n]" and  
    // initialize all entries it as true. A value  
    // in prime[i] will finally be false if i is  
    // Not a prime, else true.  
    $prime = array_fill(0, $n + 1, true);  
      
    for ($p = 2; $p * $p <= $n; $p++)  
    {  
        // If prime[p] is not changed, then  
        // it is a prime  
        if ($prime[$p])  
        {  
            // Update all multiples of p  
            for ($i = $p * 2; $i <= $n; $i += $p) 
            {  
                $prime[$i] = false; 
            }  
        }  
    }  
  
    // Print all palindromic prime numbers  
    for ($p = 2; $p <= $n; $p++) 
    {  
  
    // checking whether the given number   
    // is prime palindromic or not  
    if ($prime[$p] && isPal($p)) 
    {  
        print($p . " ");  
    }  
    }  
}  
  
// Driver Code 
$n = 100;  
print("Palindromic primes smaller " .  
      "than or equal to ".$n." are :\n");  
printPalPrimesLessThanN($n);  
  
// This code is contributed by mits  
?> 

Output:

Palindromic primes smaller than or equal to 100 are :
2 3 5 7 11

This article is contributed by Rahul Agrawal .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.

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