Find Next Palindrome Prime in C++

In this problem, we are given an element N. We need to find the next palindrome prime.

Problem Description − We need to find the smallest prime number which is also a palindrome number, greater than N.

Palindrome Number is a number in which the numbers are the same in both directions.

Prime Number is a number if its only factors are 1 and itself.

Let’s take an example to understand the problem,

Input

N = 12

Output

101

Explanation

The series of palindromes greater than 12 are 22, 33, 44, 55, 66, 77, 88, 99, 101… out of these the smallest palindrome is 101.

Solution Approach

A simple solution to the problem is by finding all palindromes greater than N that are primes.

A more efficient solution is by finding the even digit palindrome which is multiple of 11.

Here is a proof of this solution,

11% 11 = 0
1111% 11 = 0

Using this we will find palindrome with even digits −

xyzzyx % 11 = 0, which makes all even number digits not palindrome.

Program to illustrate the working of our solution,

Example

#include <iostream>
#include <string>
using namespace std;
bool isPrime(int num) {
   if (num < 2 || num % 2 == 0)
      return num == 2;
   for (int i = 3; i * i <= num; i += 2)
      if (num % i == 0)
         return false;
   return true;
}
int primePalindrome(int N) {
   if (8 <= N && N <= 11)
      return 11;
   for (int x = 1; x < 100000; ++x) {
      string s = to_string(x), r(s.rbegin(), s.rend());
      int y = stoi(s + r.substr(1));
      if (y >= N && isPrime(y))
         return y;
   }
   return -1;
}
int main() {
   int N = 432;
   cout<<"The next prime palindrome is "<<findNextPrimePallindrome(432);
   return 0;
}

Output

The next number with same set of digits is 92543