I looked up pseudoprimes on Wikipedia and found out just how rare 2-pseudoprimes are: there are only 3 below 1000 and only 245 below a million. That's why it amazes me that there are infinitely many 2-pseudoprimes. Actually, when reading the wikipedia page, I found out that there are infinitely many pseudoprimes of "a given base"… I take that to mean that there are infinitely many of any base. Anybody else have an opinion on how to understand that?

By the way, I originally googled "'fake' primes" and the first website that showed up was the lecture notes from this wiki!