in our NT course we have the topic arithmetic progressions and we had to prove that there are infinitely many primes in the progressions and .
Now the task says to find more arithmetic progressions containing infinitely primes. Our professor said at some point that every arithmetic progression(a. p.) contains infinitely many primes, but is it also possible to find a non-difficult proof that there are infinitely many a. p. with infinitely many primes? I thought about , ... but the proof for the cases and were a bit longer, is there a possibility to generalize them for ?
I would be thankful for any help I can get.