You need to be a little tighter. You start by assuming that there is a finite number of primes, and that p1, p2, …pn is a list of _all_ the primes—that’s it, there are no more. Then you show that that assumption can’t be true, because there must be another prime that wasn’t in your list. And even if you add this new prime to your list, there must be yet another, and so on…