Two points: A) Euclid never assumes the existence of a finite set of all primes (doing so at the outset is a framing adopted only by later mathematicians); peo

Two points: A) Euclid never assumes the existence of a finite set of all primes (doing so at the outset is a framing adopted only by later mathematicians); people just frequently erroneously think Euclid's proof did this, never having actually read it. Rather, Euclid constructively frames things, directly arguing that, for any finite set of primes, there is furthermore some prime outside that set. See http://aleph0.clarku.edu/~djoyce/elements/bookIX/propIX20.html http://aleph0.clarku.edu/~djoyce/elements/bookIX/propIX20.ht.... B) Regardless, I don't particularly care how Euclid phrased his proof; I never mentioned Euclid. Certainly, mathematicians have been aware that Euclid's insight could be framed in the way I called an "old proof" for a long, long time. The distinctions between the various framings here are trivial.