Found with PFGW Version 3.7.5

3145^9396-9396^3145 is 2-PRP! (21.3852s+0.0014s)
3145^9396-9396^3145 is 3-PRP! (21.5033s+0.0014s)
3145^9396-9396^3145 is 5-PRP! (21.3489s+0.0013s)
3145^9396-9396^3145 is 7-PRP! (21.2112s+0.0015s)
3145^9396-9396^3145 is 11-PRP! (21.3725s+0.0013s)

Primality testing 3145^9396-9396^3145 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 7
Running N+1 test using discriminant 17, base 8+sqrt(17)
Calling N-1 BLS with factored part 0.03% and helper 0.02% (0.12% proof)
3145^9396-9396^3145 is Fermat and Lucas PRP! (104.5629s+0.0022s)

To be completed...