Found with PFGW Version 3.8.0

8^85349-85349^8 is 2-PRP! (113.2429s+0.0038s)
8^85349-85349^8 is 3-PRP! (112.7565s+0.0043s)
8^85349-85349^8 is 5-PRP! (114.4509s+0.0068s)
8^85349-85349^8 is 7-PRP! (110.3083s+0.0069s)
8^85349-85349^8 is 11-PRP! (112.1234s+0.0058s)

Primality testing 8^85349-85349^8 [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 discriminant 13, base 2+sqrt(13)
Calling N-1 BLS with factored part 0.02% and helper 0.01% (0.06% proof)
8^85349-85349^8 is Fermat and Lucas PRP! (752.7676s+0.0047s)

To be completed...