[coloradan]

Yes, 16 is dividable - but not by 3 nor 5. What I wrote was, the new number is either prime, or it's a composite number containing prime factors not on your original list. The latter is the case here - 2 wasn't on your list. Let's do this again, now knowing of 2, 3, and 5. Their product is 30. Adding one makes 31. In this case, it's a new prime. You will never, ever run out: this process will always generate new primes, or composite numbers with all-new prime factors. On the other hand, this process doesn't guarantee it will generate a complete set - only that the set is infinite.

[P.O.E.]

I figured I wasn't following you correctly - and I was right. I wasn't correctly following you!

Got it now - thanks :)