Palindromic Primes


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

Below is the C++ implementation of above algorithm:

// C++ Program to print all palindromic primes
// smaller than or equal to n.
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 = 200;
    printf("Palindromic primes smaller than or "
           "equal to %d are :\n", n);


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 or mail your article to See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.

GATE CS Corner    Company Wise Coding Practice

Recommended Posts:

3 Average Difficulty : 3/5.0
Based on 3 vote(s)

Writing code in comment? Please use, generate link and share the link here.