Found with PFGW Version 3.8.0

496^31671+31671^496 is 2-PRP! (147.3594s+0.0049s)
496^31671+31671^496 is 3-PRP! (142.6791s+0.0044s)
496^31671+31671^496 is 5-PRP! (147.0821s+0.0058s)
496^31671+31671^496 is 7-PRP! (146.8807s+0.0128s)
496^31671+31671^496 is 11-PRP! (150.2961s+0.0059s)

Primality testing 496^31671+31671^496 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 11, base 1+sqrt(11)
Calling N+1 BLS with factored part 0.01% and helper 0.01% (0.02% proof)
496^31671+31671^496 is Fermat and Lucas PRP! (723.0890s+0.0056s)

To be completed...