For many integer sequences $X=(x_n)_n$, it is a natural question to describe the set $P_X$ of all prime numbers $p$ that divide some non-zero term of the sequence, and to quantify the `size' of $P_X$. \\ \noindent We focus on the case of linear recurrent sequences, where we have fairly complete results for recurrences of order 2 based on the Chebotarev density theorem, and mostly open questions for higher order recurrences.