Found with PFGW Version 3.7.5

6747^8188-8188^6747 is 2-PRP! (41.4065s+0.0033s)
6747^8188-8188^6747 is 3-PRP! (40.9655s+0.0033s)
6747^8188-8188^6747 is 5-PRP! (39.8939s+0.0030s)
6747^8188-8188^6747 is 7-PRP! (40.0771s+0.0032s)
6747^8188-8188^6747 is 11-PRP! (41.1462s+0.0032s)

Primality testing 6747^8188-8188^6747 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 13, base 1+sqrt(13)
Calling N-1 BLS with factored part 0.05% and helper 0.01% (0.15% proof)
6747^8188-8188^6747 is Fermat and Lucas PRP! (236.3638s+0.0051s)

To be completed...