On prime non-primitive von Neumann regular algebras
  Let $E$ be any directed graph, and $K$ any field. We classify those graphs $E$ for which the Leavitt path algebra $L_K(E)$ is primitive. As a consequence, we obtain classes of examples of von Neumann regular prime rings which are not primitive. 
Gene Abrams, Jason Bell, and Kulumani M. Rangaswamy
math.RA