C++ Program: Check if a Number is Prime

Program Code:

#include <iostream>
#include <cmath> // For sqrt function

using namespace std;

// Function to check if a number is prime
bool isPrime(int n) {
    // Corner cases
    if (n <= 1) {
        return false;
    }
    if (n <= 3) {
        return true;
    }

    // Check for divisibility from 2 to sqrt(n)
    for (int i = 2; i <= sqrt(n); i++) {
        if (n % i == 0) {
            return false;
        }
    }
    return true;
}

int main() {
    int number;
    cout << "Enter a number: ";
    cin >> number;

    // Check if number is prime and display result
    if (isPrime(number)) {
        cout << number << " is a prime number." << endl;
    } else {
        cout << number << " is not a prime number." << endl;
    }

    return 0;
}

Explanation of the Program

1. Function isPrime:
   • bool isPrime(int n): This function takes an integer n as input and returns true if n is a prime number, and false otherwise.
   • Edge Cases: Numbers less than or equal to 1 (n <= 1) are not prime.
   • Optimization: For numbers greater than 1, the function checks divisibility from 2 up to the square root of n (sqrt(n)). This optimization reduces the number of checks needed.
2. Main Function:
   • Prompts the user to enter a number.
   • Calls the isPrime function to check if the entered number is prime.
   • Displays the result based on the return value of isPrime.