Found with PFGW Version 3.7.5

10099^10304-10304^10099 is 2-PRP! (35.5764s+0.0020s)
10099^10304-10304^10099 is 3-PRP! (35.6740s+0.0019s)
10099^10304-10304^10099 is 5-PRP! (35.9200s+0.0019s)
10099^10304-10304^10099 is 7-PRP! (36.0225s+0.0018s)
10099^10304-10304^10099 is 11-PRP! (35.5360s+0.0017s)

Primality testing 10099^10304-10304^10099 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 17, base 10+sqrt(17)
Calling N+1 BLS with factored part 0.01% and helper 0.01% (0.05% proof)
10099^10304-10304^10099 is Fermat and Lucas PRP! (179.5275s+0.0025s)

To be completed...