For quite a while, I knew of only one proof of the "infinitude of
primes", namely Euclid's proof. Over the years, I've come across others,
and I've noticed that several of them are really relying on deriving a
contradiction from a particular consequence of assuming that there are
finitely many primes. That consequence, and various ways of disproving
it, are the subject of this essay.

It's at
<http://www.gbbservices.com/math/primes.html>

Hope you enjoy it,

Walter