Uncovering the Secrets of Prime Numbers

Prime numbers have long fascinated mathematicians and programmers alike. A positive integer that is only divisible by 1 and itself, prime numbers play a crucial role in various mathematical concepts and real-world applications.

What Makes a Number Prime?

To understand what constitutes a prime number, let’s consider an example. The number 13 is prime because it can only be divided by 1 and 13 itself. On the other hand, 15 is not prime because it can be divided by 1, 3, 5, and 15. Note that 0 and 1 are not considered prime numbers.

A C++ Program to Check Prime Numbers

Let’s dive into a C++ program that takes a positive integer from the user and determines whether it’s a prime number or not. The program uses a boolean variable is_prime initialized to true at the beginning.

#include <iostream>

using namespace std;

int main() {
    int n;
    bool is_prime = true;

    cout << "Enter a positive integer: ";
    cin >> n;

    if (n <= 1) {
        is_prime = false;
    } else {
        for (int i = 2; i <= n / 2; ++i) {
            if (n % i == 0) {
                is_prime = false;
                break;
            }
        }
    }

    if (is_prime) {
        cout << n << " is a prime number." << endl;
    } else {
        cout << n << " is not a prime number." << endl;
    }

    return 0;
}

The Logic Behind the Program

First, the program checks if the input number is 0 or 1, in which case is_prime is set to false. Then, a for loop is executed, which checks if the input number is perfectly divisible by any number i from 2 to n/2. If the number is divisible, is_prime is set to false, indicating that the number is not prime. However, if the number remains indivisible throughout the loop, it means that the input number is only divisible by 1 and itself, making it a prime number.

Special Cases

Interestingly, in the cases of n == 2 and n == 3, the for loop doesn’t run, and is_prime remains true. This is because these numbers are indeed prime.

Taking it Further

Want to explore more C++ programs related to prime numbers? Check out our other articles on:

• creating a function to check prime numbers
• determining whether a number can be expressed as the sum of two prime numbers