There exists a prime congruent to $m$ mod $p$ 
Q: Is every element of $\mathbb Z/p\mathbb Z$ represented by a prime number? More generally, let $m, n \in \mathbb Z$ be coprime. Is there a prime number congruent to $m$ modulo $n$?

the affirmative answer is given by Dirichlet's theorem.

Yes, in fact there are infinitely many such primes.

I don't want to prove Dirichlet's theorem. Is it obvious that there always exists at least one such prime?
