bool function for prime numbers

Question

I have the following code for checking whether the first 20 positive numbers are prime using a bool function.

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

bool prime(int);
/* 
function to evaluate whether a positive integer is prime (true)
or not prime (false)
*/
int main()
{
    for(int x=1; x<=20; x++)
    {
        cout <<  x << " a prime ? (1 yes, 0 no) "
             << prime(x) << endl;
    }
    return 0;
}

bool prime(int x)
{
    for(int i=2; i<= sqrt(x); i++)
    {
        if ((x%i) != 0)
            return true;
        else
            return false;
    }
}

It works for all numbers 1 to 20 apart from 2 and 3 where the output is 0 instead of 1. I think I know why. For x = 2 and 3 there is no i in the for loop such that i<=sqrt(2) or i<=sqrt(3).

How could I modify the code so it would work for these values too?

Also there is an error message "Control may reach end of non-void function". Why is this?

Thanks.

Answer 1

Modify your prime function to the following

bool prime(int x)
{
  if (x < 2) return false;
  for(int i=2; i<= sqrt(x); i++) {
    if ((x%i) == 0) return false;
  }
  return true;
}

The Control may reach end of non-void function error message tells you that your prime function does not return in all cases (When you pass 1 to your function, it does not go in the for loop, and so exit without explicitly returning anything, which could lead to undefined-behavior). In general, you want to have a return instruction outside of any conditionnal structure.