Found with PFGW Version 3.7.5

303^8630-8630^303 is 2-PRP! (8.6937s+0.0010s)
303^8630-8630^303 is 3-PRP! (8.6960s+0.0010s)
303^8630-8630^303 is 5-PRP! (8.6796s+0.0009s)
303^8630-8630^303 is 7-PRP! (8.6344s+0.0010s)
303^8630-8630^303 is 11-PRP! (8.6768s+0.0017s)

Primality testing 303^8630-8630^303 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 7
Running N+1 test using discriminant 13, base 6+sqrt(13)
Calling N-1 BLS with factored part 0.05% and helper 0.02% (0.17% proof)
303^8630-8630^303 is Fermat and Lucas PRP! (42.6928s+0.0018s)

To be completed...