On the Least Prime in an Arithmetical Progression

Let k and l be integers prime to each other, of which k is positive. Dirichlet proved that there are infinitely many primes in the arithmetical progression kx+l. If P(k, l) is the least prime of this form it is probable that P(k, l)<k^1+ε for every positive ε and all large k. We are very far at present even from being able to show that P(k, l) < k^m where m is any fixed positive constant independent of k, which is large. However if we assume the truth of the so-called "extended Riemann hypothesis" we can (1) show that P(k, l)<k^2+ε for k > k₀ (ε).