  Let $p$ be a prime number, and $h$ a positive integer such that
$\gcd(p,h)=1$. We prove, without invoking Dirichlet's theorem, that the
arithmetic progression $p\left(\mathbf{N}\cup \{0\}\right)+h$ contains
infinitely many prime numbers. This is a special case of Dirichlet's theorem
not considered by other authors.
