Show that there exist infinitely many primes of the form $6k-1$ This is a question on the text book that i have no way to deal with. Can anyone help me?
Show that there exist infinitely many primes of the form $6k-1$

Hint: Suppose $p_1, \dots, p_n$ be all the primes of the form $6k-1$, then $N = 6p_1\dots p_n-1$ is also of the form $6k-1$. If $N$ is divisible by a prime, it must be $3$ or of the form $6k+1$ (why?). Show that these can't actually be factors, so $N$ is prime.
