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

Checked with PFGW (v3.7.8) in all odd prime bases < 20

lucasU(-4263261111420568,631^11,32371) is 3-PRP! (8842.9727s+0.0341s)
lucasU(-4263261111420568,631^11,32371) is 5-PRP! (7262.3526s+0.0303s)
lucasU(-4263261111420568,631^11,32371) is 7-PRP! (7267.8255s+0.0301s)
lucasU(-4263261111420568,631^11,32371) is 11-PRP! (7252.3667s+0.0298s)
lucasU(-4263261111420568,631^11,32371) is 13-PRP! (7272.8537s+0.0299s)
lucasU(-4263261111420568,631^11,32371) is 17-PRP! (7274.7354s+0.0302s)
lucasU(-4263261111420568,631^11,32371) is 19-PRP! (7261.2262s+0.0298s)

and Pari/GP (v2.5.5)

? ispseudoprime(abs(lr(631,32371)))
time = 79h, 24min, 7,227 ms.
%37 = 1

To be completed...