C++ program printing one more prime value that it should

Question

Here I have a C++ program that prints 2 to n prime numbers. The problem is, it is printing one digit more than what it needs to. Ex: n = 20 and it prints up to 23 instead of stopping at 19.

#include <iostream>
#include <cmath>
using namespace std;

int main()
{
    int n, status = 1, num = 3, count, c;
    // User input to get n
    cout << "Enter n: ";
    cin >> n;

    // Input is a possible prime number
    if (n >= 1){
        // Print 2 as the first prime number
        cout << 2 << endl;
    }
    // loop that will iterate through n numbers
    for (count = 2 ; count <=n ;){
        // for each element check whether it is prime or not
        for (c = 2 ; c <= (int)sqrt(num) ; c++){
            // Not a prime number if divisble by something other than 1 or itself
            if (num%c == 0){
                status = 0;
                break;
            }
        }
        // Print prime numbers
        if (status != 0){
            cout << num << endl;
            count++;
            // If printed number is greater than n, stop the loop and printing
            if (num >= n){
                status = 0;
                break;
            }
        }
        status = 1;
        num++;
    }         

    return 0;
}

Answer 1

The problem lies with this section:

// Print prime numbers
if (status != 0){
    cout << num << endl;
    count++;
    // If printed number is greater than n, stop the loop and printing
    if (num >= n){
        status = 0;
        break;
    }
}

Since you check if num exceeds your end n only after you print the number, you'll end up printing one extra prime number. To fix this, you could simply rearrange your code a little, to only print after checking the condition:

// Print prime numbers
if (status != 0){
    // If number is greater than n, stop the loop and printing
    if (num > n){
        status = 0;
        break;
    }

    cout << num << endl;
    count++;
}

Note how I also changed the num >= n to just num > n. This will ensure that if n is a prime number, it will still be printed. (So the maximum of the range you specify will be inclusive.) Hope this helped! Let me know if you have any questions.

Answer 2

This

    // Print prime numbers
    if (status != 0){
        cout << num << endl;
        count++;
        // If printed number is greater than n, stop the loop and printing
        if (num >= n){
            status = 0;
            break;
        }
    }
    status = 1;
    num++;

should be

    // Print prime numbers
    if (status != 0){
        cout << num << endl;
        count++;
        // If printed number is greater than n, stop the loop and printing
    }
    if (num >= n){
        status = 0;
        break;
    }
    status = 1;
    num++;

Answer 3

You should use "num" not "count" in loop condition.

while (num <= n){
        // for each element check whether it is prime or not
        for (c = 2 ; c <= (int)sqrt(num) ; c++){
            // Not a prime number if divisble by something other than 1 or itself
            if (num%c == 0){
                status = 0;
                break;
            }
        }
        // Print prime numbers
        if (status != 0){
            cout << num << endl;
        }
        status = 1;
        num++;
    }