Found with PFGW Version 3.7.5

303^9806-9806^303 is 2-PRP! (10.1913s+0.0012s)
303^9806-9806^303 is 3-PRP! (10.1494s+0.0011s)
303^9806-9806^303 is 5-PRP! (10.0900s+0.0011s)
303^9806-9806^303 is 7-PRP! (10.0164s+0.0011s)
303^9806-9806^303 is 11-PRP! (10.0635s+0.0010s)

Primality testing 303^9806-9806^303 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 19, base 2+sqrt(19)
Calling N-1 BLS with factored part 0.01% and helper 0.01% (0.05% proof)
303^9806-9806^303 is Fermat and Lucas PRP! (50.5039s+0.0019s)

To be completed...