>>12840565This is the fastest proof if you accept that reducible implies prime over the integers, but anon has to point out that neither 2 nor 3 are units as well.
Otherwise, a prime p is said to prime if p|ab implies p|a or p|b. Notice that 6|(2 * 3) but 6 does not divide neither 2 nor 3 as a|b requires that |a| is at most |b| and |2| < |6| and |3| < |6|. Therefore 6 is not prime.
