Example: Check if a Number is Sum of Two Primes in C++

// Check if a Number is Sum of Two Primes
#include <iostream> // For input/output operations
#include <cmath>    // For sqrt function

// Function to check if a number is prime
bool isPrime(int num) {
    // Step 1: Handle edge cases for primality
    if (num <= 1) {
        return false; // Numbers less than or equal to 1 are not prime
    }
    // Step 2: Check divisibility from 2 up to the square root of num
    // We only need to check up to sqrt(num) because if num has a divisor
    // greater than sqrt(num), it must also have one smaller than sqrt(num).
    for (int i = 2; i <= sqrt(num); ++i) {
        if (num % i == 0) {
            return false; // If divisible, it's not prime
        }
    }
    // Step 3: If no divisors found, it's prime
    return true;
}

int main() {
    int n;
    // Step 1: Prompt user for input
    std::cout << "Enter a positive integer: ";
    std::cin >> n;

    // Step 2: Check if the number can be expressed as sum of two primes
    bool found = false; // Flag to track if a pair is found
    for (int i = 2; i <= n / 2; ++i) {
        // Step 3: Check if 'i' is prime
        if (isPrime(i)) {
            // Step 4: Check if 'n - i' is prime
            if (isPrime(n - i)) {
                // Step 5: If both are prime, print the result and set flag
                std::cout << n << " can be expressed as sum of two prime numbers: " << i << " + " << (n - i) << std::endl;
                found = true;
                break; // Found a pair, no need to check further
            }
        }
    }

    // Step 6: If no pair was found after checking all possibilities
    if (!found) {
        std::cout << n << " cannot be expressed as sum of two prime numbers." << std::endl;
    }

    return 0; // Indicate successful execution
}