Found with PFGW Version 3.7.5

7648^9543-9543^7648 is 2-PRP! (25.5331s+0.0014s)
7648^9543-9543^7648 is 3-PRP! (25.5357s+0.0015s)
7648^9543-9543^7648 is 5-PRP! (26.0304s+0.0016s)
7648^9543-9543^7648 is 7-PRP! (25.4231s+0.0015s)
7648^9543-9543^7648 is 11-PRP! (25.6310s+0.0016s)

Primality testing 7648^9543-9543^7648 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N-1 test using base 11
Running N-1 test using base 13
Running N+1 test using discriminant 23, base 2+sqrt(23)
Calling N-1 BLS with factored part 0.02% and helper 0.01% (0.06% proof)
7648^9543-9543^7648 is Fermat and Lucas PRP! (198.9344s+0.0023s)

To be completed...