Suppose you were asked to find the smallest positive primitive root g mod 9973. What candidate values of g below 12 would you need to test (assuming every one you tested, starting with 2, 3, ..., gave a negative answer, and so you constantly had to go to the next one), and what steps would you need to take to test each candidate g? No need to do any actual computations. (As it turns out, 11 is the smallest positive primitive root, so in principle you have to consider all g < 12, but some can be eliminated from consideration using theory and tests of smaller candidate values.)