C++ Exercises: Check Whether a Number can be Express as Sum of Two Prime Numbers

Last update on April 07 2025 12:59:35 (UTC/GMT +8 hours)

33. Express a Number as the Sum of Two Primes

Write a program in C++ to check whether a number can be expressed as the sum of two.

Visual Presentation:

C++ Exercises: Check Whether a Number can be Express as Sum of Two Prime Numbers

Sample Solution:-

C++ Code :

#include <iostream> // Include the input/output stream library
using namespace std; // Using standard namespace

int main() // Main function where the execution of the program starts
{
    int n, i, flg1 = 1, flg2 = 1, flg3 = 0, j; // Declare integer variables n, i, flg1, flg2, flg3, j
    float sum = 0; // Declare and initialize a float variable sum to 0

    // Display message asking for input
    cout << "\n\n Check Whether a Number can be Express as Sum of Two Prime Numbers:\n";
    cout << "------------------------------------------------------------------------\n";
    cout << " Input  a positive integer: ";
    cin >> n; // Read input for a positive integer

    // Loop to find two prime numbers whose sum equals the input number
    for (i = 2; i <= n / 2; i++) 
    {
        /*---------- check for prime---------------*/
        flg1 = 1; // Initialize flg1 as 1 (considering the number is prime)
        flg2 = 1; // Initialize flg2 as 1 (considering the number is prime)

        // Loop to check if 'i' is a prime number
        for (j = 2; j < i; j++) 
        {
            if (i % j == 0) // If 'i' is divisible by any number other than 1 and itself
            {
                flg1 = 0; // Set flg1 as 0 (indicating 'i' is not prime)
                j = i; // Exit the loop
            }
        }

        // Loop to check if 'n - i' is a prime number
        for (j = 2; j < n - i; j++) 
        {
            if ((n - i) % j == 0) // If 'n - i' is divisible by any number other than 1 and itself
            {
                flg2 = 0; // Set flg2 as 0 (indicating 'n - i' is not prime)
                j = n - i; // Exit the loop
            }
        }

        // If both 'i' and 'n - i' are prime numbers, print their sum as 'n'
        if (flg1 == 1 && flg2 == 1) 
        {
            cout << n << " = " << i << " + " << n - i << endl; // Display the expression of 'n' as sum of two prime numbers
            flg3 = 1; // Set flg3 as 1 to indicate a successful expression of 'n'
        }
    }

    // If 'n' cannot be expressed as the sum of two prime numbers, display a message
    if (flg3 == 0) 
    {
        cout << n << " can not be expressed as sum of two prime numbers." << endl; // Display that 'n' cannot be expressed as the sum of two prime numbers
    }
}

Sample Output:

 Check Whether a Number can be Express as Sum of Two Prime Numbers:    
------------------------------------------------------------------------                                                                      
 Input  a positive integer: 20                                         
20 = 3 + 17                                                            
20 = 7 + 13

Flowchart:

For more Practice: Solve these Related Problems:

Write a C++ program to check if a given number can be expressed as the sum of two prime numbers and list the pairs if possible.
Write a C++ program that reads an even integer and outputs all pairs of prime numbers whose sum equals that number.
Write a C++ program to generate prime numbers within a range and then check for pairs that sum up to a specified target.
Write a C++ program to find and display all combinations of two primes that add up to an input number, if any exist.

C++ Code Editor:

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