According to PFGW, Fermat and Lucas PRP.

A PRP of the form p = a^2 + k^n = b^2 + k^m - see this posting by David Broadhurst and Mike Oakes:
http://listserv.nodak.edu/cgi-bin/wa.exe?A2=ind0607&L=nmbrthry&P=R1286

To be completed...