C++ Program To Check If a Prime Number Can Be Expressed as Sum of Two Prime Numbers

Given a prime number . The task is to check if it is possible to express as sum of two separate prime numbers.
Note: The range of N is less than 10⁸.

Examples:

Input: N = 13
Output: Yes
Explanation: The number 13 can be written as 11 + 2, 
here 11 and 2 are both prime.

Input: N = 11
Output: No

Simple Solution: A simple solution is to create a sieve to store all the prime numbers less than the number N. Then run a loop from 1 to N and check whether and are both prime or not. If yes then print Yes, else No.

Efficient solution: Apart from 2, all of the prime numbers are odd. So it is not possible to represent a prime number (which is odd) to be written as a sum of two odd prime numbers, so we are sure that one of the two prime number should be 2. So we have to check whether n-2 is prime or not. If it holds we print Yes else No.
For example, if the number is 19 then we have to check whether 19-2 = 17 is a prime number or not. If 17 is a prime number then print yes otherwise print no.

Below is the implementation of the above approach: 

C++

// C++ program to check if a prime number
// can be expressed as sum of
// two Prime Numbers
#include <bits/stdc++.h>
using namespace std;

// Function to check whether
// a number is prime or not
bool isPrime(int n)
{
    if (n <= 1)
        return false;

    for (int i = 2; i <= sqrt(n); i++)
    {
        if (n % i == 0)
            return false;
    }

    return true;
}

// Function to check if a prime number
// can be expressed as sum of
// two Prime Numbers
bool isPossible(int N)
{
    // if the number is prime,
    // and number-2 is also prime
    if (isPrime(N) && isPrime(N - 2))
        return true;
    else
        return false;
}

// Driver code
int main()
{
    int n = 13;

    if (isPossible(n))
        cout << "Yes";
    else
        cout << "No";

    return 0;
}

Output:

Yes