  We give an explicit version of Brun-Titchmarsh theorem applicable for
arbitrary moduli and arbitrary intervals. For example, we show that $\pi(x+y;
k, a)-\pi(x; k, a)<2y/(\varphi(k)(\log (y/k)+0.8601))$ for any relatively prime
positive integers $k$ and $a$ and any positive real numbers $x$ and $y$ such
that $y>k$.
