Prime numbers

All right, in this lesson we are going to write a program that has functions and figures out whether or not a number is prime.

A natural number is prime if it is greater than 1 and has no divisors other than 1 and itself.

Prime numbers are numbers that are not divisible by any other number besides 1
Lets take 7 for example.....
     7 is divisible 1.  no big deal
     7 is not divisible by 2... good
     7 is not divisible by 3... good
     7 is not divisible by 4... good
     7 is not divisible by 5... good
     7 is not divisible by 6... good
Sooo 7 is a prime number

Lets take 6 for example
     6 is divisible by 1. no big deal
     6 is divisible by 2... so
     6 is divisible by 3... so
6 is NOT a prime number

Is it important to divide a number by every number between 1 and itself?
     No...
It is only important to divide the number in question up to half of its value.
     the other numbers above its half way will just be a repeat of the lower half

Sooo we could take the square root of a number 
     for example the square root of 25 is 5
     and run the code up to that point, to test if the number for divisibility.

Your task is to write a function that checks whether or not a number is prime or not.
The function: is called "isPrime";
takes one int argument (the value to check);
returns "true" if the argument is a prime number or "false" otherwise;
should be mute.

Hint: try to divide the argument by all subsequent values (starting from 2) and check the remainder – if it's 0, your number cannot be a prime;
think carefully when you should stop the process and check whether you could use the "sqrt()" function
(which you already know).

Complete the code below.

​Run your code and check whether your output is the same as ours.

Sample code

#include <iostream>
#include <cmath>

using namespace std;

bool isPrime(int num)
{

     // Insert your code here

}

int main(void)
{

     for(int i = 0; i <= 21; i++)

          if(isPrime(i))
               cout << i << " ";

     cout << endl;
     return 0;
} ​

​

Sample Output

2 3 5 7 11 13 17 19