For those familiar with Euclid’s proof of the infinitude of prime numbers, this video will be a treat. All odd primes leave a residue of $1$ or $3$ modulo $4$. With a slight modification of Euclid’s proof, we can show that there exist infinitely many primes congruent to $3$ modulo $4$, which is what we do in this video. We challenge the audience to adapt the proof in the $5$ modulo $6$ case.