No, it follows directly from the fact that the positive integers are well-ordered, i.e., any set of positive integers has a least element.<p>And in case one is tempted to think that well-ordering and divisibility are somehow equivalent, consider Presburger arithmetic[1]. It&#x27;s not even possible to define a general notion of divisibility or primality in that context, but I&#x27;m almost positive the well-ordering principle holds (it&#x27;s equivalent to the axiom schema of induction).<p>[1]: <a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Presburger_arithmetic" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Presburger_arithmetic</a>