Balanced Prime in C++

Balanced prime number is a prime number that has the same difference for its previous and next prime numbers. i.e. it is the mean of the nearest next prime and previous prime.

For a prime number to be a balanced prime, it should follow the following formula −

P_n = (P(n-1) + P(n+1)) / 2

Where n is the index of the prime number pn in the ordered set of a prime number.

The ordered set of prime numbers: 2, 3, 5, 7, 11, 13,….

First, balanced primes are 5, 53, 157, 173 , …

In this problem, we are given a number n and we have to find an nth balanced prime number.

Let’s take an example,

Input : n = 3
Output : 157

For this will generate prime numbers and store it in an array. We will find whether the prime number is a balanced prime or not. If it increases the count and if the count is equal to n, print it.

Example

 Live Demo

#include<bits/stdc++.h>
#define MAX 501
using namespace std;
int balancedprimenumber(int n){
   bool prime[MAX+1];
   memset(prime, true, sizeof(prime));
   for (int p = 2; p*p <= MAX; p++){
      if (prime[p] == true)
      {
         for (int i = p*2; i <= MAX; i += p)
         prime[i] = false;
      }
   }
   vector<int> v;
   for (int p = 3; p <= MAX; p += 2)
   if (prime[p])
   v.push_back(p);
   int count = 0;
   for (int i = 1; i < v.size(); i++){
      if (v[i] == (v[i+1] + v[i - 1])/2)
      count++;
      if (count == n)
      return v[i];
   }
}
int main(){
   int n = 3;
   cout<<balancedprimenumber(n)<<endl;
   return 0;
}

Output

157