Found with PFGW Version 3.7.5

3222^9401-9401^3222 is 2-PRP! (38.8188s+0.0021s)
3222^9401-9401^3222 is 3-PRP! (40.4001s+0.0023s)
3222^9401-9401^3222 is 5-PRP! (40.9622s+0.0021s)
3222^9401-9401^3222 is 7-PRP! (35.6251s+0.0025s)
3222^9401-9401^3222 is 11-PRP! (44.7484s+0.0022s)

Primality testing 3222^9401-9401^3222 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 7
Running N-1 test using base 11
Running N+1 test using discriminant 19, base 1+sqrt(19)
Calling N+1 BLS with factored part 0.03% and helper 0.02% (0.13% proof)
3222^9401-9401^3222 is Fermat and Lucas PRP! (209.5934s+0.0031s)

To be completed...