# Tag Info

To prove that $$\frac{\#(\text{primes}~~ qn+a \leq x)}{\pi(x)/\phi(q)}\to 1~ \text{as} ~ x\to \infty,$$ that there are roughly the same number of primes in each residue class $a$ if $(a,q)=1$ without some version of Dirichlet characters/series might be hard. There is no special virtue of using $Li(x)$ here, any function $\sim \pi(x)$ will work. ...