Yet another Greek.
Quidquid id est, timeo Danaos et dona ferentes
OK, but how does that jibe with the cartoon I've quoted above?
(BTW, thanks for that reference, it was very interesting. )
Sorry George, I forgot you're a philosopher, not a mathematician
The cartoon summarizes Euclid's (yep, yet another pesky Greek's) proof that the primes go on forever:
Call the primes in our finite list p1, p2, ..., pr. Let P be any common multiple of these primes plus one (for example, P = p1p2...pr+1). Now P is either prime or it is not. If it is prime, then P is a prime that was not in our list. If P is not prime, then it is divisible by some prime, call it p. Notice p can not be any of p1, p2, ..., pr, otherwise p would divide 1, which is impossible. So this prime p is some prime that was not in our original list. Either way, the original list was incomplete.
And, btw, even the original of your "...timeo Danaos..." was written by yet another Greek - you can't win this one easily....