Is the language of primitive words context‑free (over non‑unary alphabets)?

Determine whether the language of primitive words over any non‑unary alphabet is context‑free.

Background

The paper studies probabilistic membership for the language of primitive words (non‑proper powers) and provides a tractable algorithm via circuits with complementation. However, the longstanding question of whether this language is context‑free over non‑unary alphabets remains unresolved.

Settling context‑freeness would clarify the placement of this classical language within the Chomsky hierarchy and inform which grammar‑based techniques could apply.