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Check if a Number is Prime with Simple C++ Code

Determining whether a number is prime is a common task in programming and mathematics. A prime number is defined as a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers. In this blog post, we’ll explore a straightforward C++ code snippet that checks if a given number is prime or not.

#include<iostream>
using namespace std;

main()
{
    int n, num = 2, flag = 0;
    cin >> n; // Read an integer from user input

    // Check for primality
    while (num < n)
    {
        if (n % num == 0)
        {
            cout << "Not Prime" << endl; // Print "Not Prime" if 'n' is divisible by 'num'
            flag = 1; // Set flag to 1 indicating that 'n' is not prime
            break; // Exit the loop as we have found a divisor
        }
        num++; // Increment 'num' to check the next divisor
    }
   
    if (flag == 0)
        cout << "Prime" << endl; // Print "Prime" if no divisors were found
}

How the Code Works

1. Input Reading

The code begins by reading an integer input from the user, which is stored in the variable n.

2. Initial Setup

  • num: This variable starts at 2 and will be used to check possible divisors of n.
  • flag: A flag is set to 0 initially. It will be used to indicate whether a divisor has been found.

3. Checking for Divisors

The code enters a while loop that runs as long as num is less than n. Inside the loop:

  • Divisibility Check: The condition if (n % num == 0) checks if n is divisible by num without leaving a remainder.
    • If True: This means n is not a prime number (as it has a divisor other than 1 and itself). The code prints "Not Prime", sets flag to 1, and breaks out of the loop.
    • If False: The loop continues with num incremented by 1 to check the next possible divisor.

4. Final Check

After the loop, if flag is still 0, it means no divisors were found other than 1 and n itself. Therefore, n is a prime number, and the code prints "Prime".

Why This Code Works

  • Efficiency: The loop runs only until num is less than n. For each iteration, it checks if n is divisible by the current num.
  • Correctness: If n is divisible by any number other than 1 and itself, it is correctly identified as "Not Prime". If no such divisors are found, n is correctly identified as "Prime".

Potential Improvements

  • Optimize Divisor Check: Instead of checking up to n, you could check up to the square root of n. This would make the code more efficient for larger numbers.
  • Edge Cases: The code does not handle numbers less than 2. It would be beneficial to include checks for such cases and handle them appropriately.

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