Determine Prime Numbers using SINGLE do-while Loop - c

Question

I wrote this program per my professor's instruction. Turns out he wanted us to use a SINGLE do-while loop. While I did technically do that... this won't fly. I can't figure out how to do it without using a for-loop or at least another loop of some other type. He said it could use continue or break statements--but that it might not be necessary.
I would appreciate not just re-writing my code--while this is handy, I don't learn from it well.
I appreciate any and all help.
int main() {
int max, x, n = 2; //init variables
//start n at 2 because 1 isn't prime ever
//asks user for max value
printf("Enter max number: ");
scanf("%i", &max);
/*prints prime numbers while the max value
is greater than the number being checked*/
do {
x = 0; //using x as a flag
for (int i = 2; i <= (n / 2); i++) {
if ((n % i) == 0) {
x = 1;
break;
}
}
if (x == 0) //if n is prime, print it!
printf("%i\n", n);
n++; //increase number to check for prime-ness
} while (n < max);
return 0;
}

Answer 1

This is definitely doable. The trick is to have a test variable, and each iteration through your while loop, check the test variable against your current number. Always start the test variable at 2 (every natural number > 0 is divisible by 1)
Cases to consider:
Our current number is divisible by the test variable -- number is NOT prime, increase the current number and reset the test variable.
Our test variable is greater than the square root of the current number. By definition, it CANNOT divide the current number, so the current number has to be prime (we have tried all numbers lower than the square root of the current number and none of them divide it). Increase the current number and reset the test variable.
Lastly, if either above case isn't true, we have to try the next number higher. Increment the test variable.
I have not provided the code as you asked to not have it re-written, but can provide if you would like.
EDIT
#include <stdio.h>
#include <math.h>
int main(void)
{
int max = 20;
int current = 4;
int checker = 2;
do{
if(checker > sqrt((double)current))
{
checker = 2;
printf("%d is prime\n",current);
current++;
}
else if(current % checker == 0)
{
checker = 2;
printf("%d is NOT prime\n",current);
current++;
}
else
checker++;
}while(current < max);
}
Output:
4 is NOT prime
5 is prime
6 is NOT prime
7 is prime
8 is NOT prime
9 is NOT prime
10 is NOT prime
11 is prime
12 is NOT prime
13 is prime
14 is NOT prime
15 is NOT prime
16 is NOT prime
17 is prime
18 is NOT prime
19 is prime

Answer 2

I won't give you the exact code, but two pointers that should help you:
First, a for loop can be written as a while loop (and, vice versa)
for (int i=0; i< 100; ++i)
...
would become:
int i=0;
while (i < 100)
{
...
++i;
}
Second, two nested loops can become a single one, in any number of ways:
for (int i=0; i< 100; ++i)
for (int j=0; j< 100; ++j)
...
Becomes
for (int z=0; z< 100*100; ++z)
{
i = z / 100;
j = z % 100;
}
The above shows two for loops, but you can perform similar transforms on other loops.

Answer 3

Think Eratosthenes sieve. In this method we strike composite numbers out of a table, so that in the end only primes remain. For simplicity, the table contains only odd numbers. You start pointing at 3, which is a prime. Strike out 3*3, 3*5... Finish your run over the table (it's finite), point at 5. It's not striked out, thus a prime. Strike out 15, 25... check 7, prime, strike 21, 35... check 9, already striked out, move on to 11...
Questions:
You have just checked a number, what is the next number to check?
How do you know you've ran out of numbers to check?
Write down answers to these questions, and you have a one-loop prime-finding algorithm.