Found with PFGW Version 3.5.2

812^3505-3505^812 is 2-PRP! (19.9286s+0.0233s)
812^3505-3505^812 is 3-PRP! (23.4243s+0.0108s)
812^3505-3505^812 is 5-PRP! (17.5338s+0.0093s)
812^3505-3505^812 is 7-PRP! (19.8451s+0.0078s)
812^3505-3505^812 is 11-PRP! (22.9171s+0.0108s)

Primality testing 812^3505-3505^812 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N-1 test using base 5
Running N-1 test using base 13
Running N+1 test using discriminant 19, base 1+sqrt(19)
Calling N+1 BLS with factored part 0.09% and helper 0.03% (0.32% proof)
812^3505-3505^812 is Fermat and Lucas PRP! (179.0168s+0.0136s)

To be completed...