This is a PRP value of the Ramanujan Tau function.
http://dx.doi.org/10.1007/s11139-012-9420-8

Verified with PFGW (v3.7.8) and Pari/GP (v2.5.5).

lucasU(303982416160892,7768205433717376298112278666107,11689) is 3-PRP! (781.5549s+0.0116s)

To be completed...