Given $a, b \in Z^+$, where $\gcd(a, b) = 1$, we can define an arithmetic sequence $c_i = a + i \cdot b$. The sequence is thus $\{a, a+b, a+2b, \cdots\}$.
Do all such sequences contain a prime? Do they contain an infinite number of primes?
Example: $a=2, b=3$. Then, $c_1 = a+b = 5$, which is prime. Meanwhile, $a=4, b=2$ does not have primes, but $\gcd(a, b) = 2 \neq 1$, so this isn't a counterexample.