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C++ Program To Check Whether a Number is Prime or not

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

Last Updated : 17 Jan, 2023

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Given a prime number [Tex]N [/Tex]. The task is to check if it is possible to express [Tex]N [/Tex]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 [Tex]i [/Tex]and [Tex]n-i [/Tex]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

C++ Program To Check Whether a Number is Prime or not

kartik

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Article Tags :

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C++ Programs
C++ Basic Programs

Practice Tags :

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