Question

A positive integer is a prime number if its only positive integer divisors are itself and 1. Write a program to determine whether or not a given integer is prime. The program should contain two functions:

main: to ask the user for a positive integer and to print the result

isPrime: to determine whether the user's input is prime by testing all possible divisors. This function should return two values:

variable_1: a Boolean value indicating whether the number is prime or not

variable_2: a numeric value indicating either the first divisor found (if the number is not prime) or the number of divisors tried (if the number is prime)

Note that the main function needs to print either of two rather different looking output messages depending on the results returned from the isPrime function.

Answer 1

C++ Function:

/* C++ Program that checks whether given number is prime or not */

#include <iostream>

using namespace std;

//Function that checks for prime number
bool isPrime(int n, int *res)
{
    int k;

    //Iterating from 2 to 1 less than the number
    for(k = 2; k <= n - 1; k++)
    {
        //If there is any divisibility, it is not a prime number
        if ( n % k == 0 )
        {
            //Storing first divisor found
            *res = k;

            //Return false
            return false;
        }

    }

    //If k is equal to n, it is a prime number
    if ( k == n )
    {
        //Updating result value
        *res = n-2;

        //Return true
        return true;
    }
}

//Main function
int main()
{
    int n, res;
    bool prime;

    //Iterate till user enters a positive integer
    do
    {
        //Reading a positive integer
        cout << "\n\n Enter a positive integer: ";
        cin >> n;

    }while(n <= 0);

    //Calling function
    prime = isPrime(n, &res);

    //If given number is prime number
    if(prime)
    {
        //Printing message
        cout << "\n\n Given number is a prime number... \n\n Total number of divisors tried: " << res << " \n";
    }
    else
    {
        //Printing message
        cout << "\n\n Given number is not a prime number... \n\n First divisor found: " << res << " \n";
    }

    return 0;
}

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Sample Output:

Answer 2

#include <iostream>
using namespace std;

bool check_prime(int);

int main() {

  int n;

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

  if (check_prime(n))
    cout << n << " is a prime number.";
  else
    cout << n << " is not a prime number.";

  return 0;
}

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

  // 0 and 1 are not prime numbers
  if (n == 0 || n == 1) {
    is_prime = false;
  }

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

  return is_prime;
}