All Questions

Let $n,a,b$ be integers such that $n$ and $a$ are coprime, and $n$ and $b$ are also coprime. According to the Prime number theorem for arithmetic progressions, the primes which are $a\mod n$ have the ...

It is mentioned in multiple occasions here that the bound $$ \mathop{\sum_{n=1}^{N}}_{n\equiv a\mod l} \mu(n) = o(N) $$ is equivalent to the prime number theorem in arithmetic progressions. But I am ...

For which sets of residue classes are there easy elementary proofs that there are infinitely many primes in them, which don’t require the machinery of proofs of Dirichlet’s theorem? Example: it’s ...

I am really interested in sufficient conditions on $a_i, b_i$ guaranteeing that the linear forms $a_1\phi(n)+b_1,\dots, a_k\phi(n)+b_k$ become simultaneously prime for infinitely many positive ...

I am currently looking for a result stronger than Siegel-Walfisz theorem, which gives an upper bound on the error term $|\pi(x,a,b)-\frac{\pi(x)}{\phi(a)}|$ for particular $a$. The Siegel Walfisz is ...