5.3.1, due November 21

In the example that went along with the first definition, is the book supposed to say that 25 is not a pseudoprime base 2 or 3? Because according to the definition you work mod n when testing n's primality. So it doesn't make sense to talk about using a different number there. So how many bases do we have to test to decide that n is pretty likely to be prime? Is there a general rule for this? And how would that work since we have lemma 5.3.1.1 where every time we test one more base, we're getting many more. Since we know that a Carmichael number must be divisible by three primes, it will never be prime. But, depending on how many units there are mod that number, it could have satisfied fermat's theorem for a lot of bases. Does that mean that purely looking at the number of bases that work for a number gives no good indication of primality?