Chapter 4.3, Problem 54E

Adapt the proof in the text that there are infinitely many primes to prove that there are infinitely many primes of the form $\text{3}k\text{+2}$ , where k is a nonnegative integer.

[Hint: Suppose that there are only finitely many such primes $q_{\text{1}}\text{,}{q}_{\text{2}},\mathrm{...},q_n$ , and consider the number $\text{3}{q}_{\text{1}}{q}_{\text{2}}\mathrm{...}{q}_n\text{-1}$ .]