Prove that the set of all prime numbers of the form $6n+5$ is infinite.
I'm thinking to show this I would consider $ab\equiv 5 \pmod 6$ so then either $a\equiv 5\pmod 6$ or $b\equiv 5 \pmod 6$. Then try to show any $d=6n+5$ is divisible by a prime of the form $p=6n_0+5$.