Formal Languages Consisting of Primitive Words

Let Q be the set of primitive words over a finite alphabet having at least two letters. We prove that Q has two rather strong context-free-like properties. The first one is that Q satisfies the nonempty, strong variant of Bader and Moura's iteration condition, and the second one is that intersecting Q with any member of a special, infinite family of regular languages, we get a context-free language. We also present two further related results. It remains an unsolved problem whether Q is non-context-free (we conjecture this).