Found with PFGW Version 3.7.5

6333^10780-10780^6333 is 2-PRP! (34.3400s+0.0017s)
6333^10780-10780^6333 is 3-PRP! (35.2331s+0.0025s)
6333^10780-10780^6333 is 5-PRP! (35.8018s+0.0025s)
6333^10780-10780^6333 is 7-PRP! (35.9299s+0.0025s)
6333^10780-10780^6333 is 11-PRP! (35.8173s+0.0025s)

Primality testing 6333^10780-10780^6333 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N-1 test using base 13
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)
6333^10780-10780^6333 is Fermat and Lucas PRP! (209.2786s+0.0028s)

To be completed...