Abstract: In 1772, Euler observed that the polynomial x2+x+41 is a remarkably rich source of primes, yielding prime values for every integer value of x from 0 to 39. A satisfying algebraic explanation for this fact was advanced by Rabinowitsch, who showed that Euler's observation is essentially equivalent to a certain ring (namely, the ring of integers of Q(sqrt(-163)) possessing unique factorization. We outline an elementary (i.e., non ideal-theoretic), geometric proof of Rabinowitsch's theorem, due to Gyarmati and Zaupper. We conclude with a discussion of principal ideal domains that are not Euclidean domains.