Abstract: Let (a_n) be a sequence of natural numbers. For a dynamical system (X,T) we will be interested in orbits of points sampled at times (a_n).

More precisely for f\in C(X) and x\in X one is interested in lim_{N\to \infty} \frac{1}{N}\sum_{n\leq N}f(T^{a_n}x). We will focus on three types of sequences that naturally arise in number theory, (i) prime numbers (ii) polynomials and (iii) products of bounded number of primes.

We will recall some known results and discuss some recent developments.