Prime Triplet in C++

In this problem, we are given a number N. Our task is to print all prime triplets less than N.

Prime triplet is a set of three prime numbers. That are of the form (p, p+2, p+6) or (p, p+4, p+6). All prime numbers are grouped according to the above triplets as every third prime in the direct pattern is a multiple of 6.

Let’s see an example to understand the problem

Input: N = 13
Output: 5 7 11

To solve this problem, we have to find all prime numbers less than equal to N. And the check for triplets.

The code to show the implementation of our solution,

Example

 Live Demo

#include <bits/stdc++.h>
using namespace std;
void findPrimes(int n, bool prime[]) {
   for (int p = 2; p * p <= n; p++) {
      if (prime[p] == true) {
         for (int i = p * 2; i <= n; i += p)
         prime[i] = false;
      }
   }
}
void printPrimeTriplets(int n) {
   bool prime[n + 1];
   memset(prime, true, sizeof(prime));
   findPrimes(n, prime);
   for (int i = 2; i <= n-6; ++i) {
      if (prime[i] && prime[i + 2] && prime[i + 6])
         cout<<i<<"\t"<<(i+2)<<"\t"<<(i+6)<<endl;
      else if (prime[i] && prime[i + 4] && prime[i + 6])
         cout<<i <<"\t"<<(i + 4)<<"\t"<<(i + 6)<<endl;
   }
}
int main() {
   int N = 15;
   cout<<"Prime Triplets Less than "<<N<<" are :\n";
   printPrimeTriplets(N);
   return 0;
}

Output

Prime Triplets Less than 15 are :
5   7   11
7   11   13