# Print all Proth primes up to N in C++

C++Server Side ProgrammingProgramming

In this problem, we are given an integer N and we have to print all proth prime numbers less than or equal to N.

## Proth Prime Number

A proth prime number is a positive integer whose value can be represented as n = k* 2n + 1. where k is an odd positive integer and n is a positive integer and both satisfy the 2n > k.

Examples − 3, 5, 13…..

Let’s take an example to understand the topic better −

Input: N = 23
Output: 3, 5, 13, 17.

For this, we will find all the prime numbers less than N(for this we will use sieve of Eratosthenes). And check if each of the prime numbers is proth number or not. And print all the proth numbers.

## Example

Live Demo

#include <bits/stdc++.h>
using namespace std;
int prime;
void SieveOfEratosthenes(int n){
for (int i = 1; i <= n + 1; i++)
prime[i] = true;
prime = false;
for (int p = 2; p * p <= n; p++) {
if (prime[p] == true) {
for (int i = p * p; i <= n; i += p)
prime[i] = false;
}
}
}
bool isTwosExponent(int n){
return (n && !(n & (n - 1)));
}
bool isaProthNumber(int n){
int k = 1;
while (k < (n / k)) {
if (n % k == 0) {
if (isTwosExponent(n / k))
return true;
}
k = k + 2;
}
return false;
}
bool isaProthPrime(int n){
if (isaProthNumber(n - 1)) {
if(prime[n])
return true;
else
return false;
}
else
return false;
}
int main(){
int n = 23;
cout<<"Proth Prime Numbers less than or equal to "<<n<<" are :\n";
SieveOfEratosthenes(n);
for (int i = 1; i <= n; i++)
if (isaProthPrime(i))
cout<<i<<"\t";
return 0;
}

## Output

Proth Prime Numbers less than or equal to 23 are −

3 5 13 17