Found with PFGW Version 3.7.5

3348^8003-8003^3348 is 2-PRP! (23.5241s+0.0021s)
3348^8003-8003^3348 is 3-PRP! (23.5980s+0.0020s)
3348^8003-8003^3348 is 5-PRP! (23.4333s+0.0020s)
3348^8003-8003^3348 is 7-PRP! (23.5542s+0.0023s)
3348^8003-8003^3348 is 11-PRP! (23.9832s+0.0040s)

Primality testing 3348^8003-8003^3348 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 11
Running N+1 test using discriminant 41, base 1+sqrt(41)
Calling N+1 BLS with factored part 0.05% and helper 0.01% (0.15% proof)
3348^8003-8003^3348 is Fermat and Lucas PRP! (120.6134s+0.0033s)

To be completed...