In the free group F k , an element is said to be primitive if it belongs to a free generating set. In this paper, we describe what a generic primitive element looks like. We prove that up to conjugation, a random primitive word of length N contains one of the letters exactly once asymptotically almost surely (as N → ∞ ). This also solves a question raised by Baumslag–Myasnikov–Shpilrain (Contemp. Math. 296 (2002) 1–38). Let p k , N be the number of primitive words of length N in F k . We show that for k ⩾ 3 , the exponential growth rate of p k , N is 2 k − 3 . Our proof also works for giving the exact growth rate of the larger class of elements belonging to a proper free factor.