Found with PFGW Version 3.6.0

3508^6933-6933^3508 is 2-PRP! (24.1259s+0.0026s)
3508^6933-6933^3508 is 3-PRP! (23.9678s+0.0026s)
3508^6933-6933^3508 is 5-PRP! (24.0316s+0.0027s)
3508^6933-6933^3508 is 7-PRP! (23.9754s+0.0029s)
3508^6933-6933^3508 is 11-PRP! (24.0421s+0.0025s)

Primality testing 3508^6933-6933^3508 [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 3+sqrt(11)
Calling N+1 BLS with factored part 0.06% and helper 0.00% (0.20% proof)
3508^6933-6933^3508 is Fermat and Lucas PRP! (141.9253s+0.0032s)

To be completed...