So the answer is we only need about 115 guesses.
So that shouldn't take too long, as long as there's a quick way to tell if a number is prime.
And to compute that result, we computed the log of 10 to the 100.
You could do that in Python by using the math library
and computing the log of 10 to the power of 100 where the base of the log is math.e--
that's the constant for the natural log.
That would give you a result about 230.
We'll divide that by 2 to get the expected number of guesses we need.