Found with PFGW Version 3.7.5

7003^8324-8324^7003 is 2-PRP! (19.5332s+0.0019s)
7003^8324-8324^7003 is 3-PRP! (19.0207s+0.0016s)
7003^8324-8324^7003 is 5-PRP! (19.1684s+0.0016s)
7003^8324-8324^7003 is 7-PRP! (19.0545s+0.0016s)
7003^8324-8324^7003 is 11-PRP! (18.9827s+0.0016s)

Primality testing 7003^8324-8324^7003 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N-1 test using base 5
Running N+1 test using discriminant 11, base 1+sqrt(11)
Calling N+1 BLS with factored part 0.03% and helper 0.02% (0.12% proof)
7003^8324-8324^7003 is Fermat and Lucas PRP! (128.0199s+0.0025s)

To be completed...