Found with PFGW Version 3.6.0

3222^3941-3941^3222 is 2-PRP! (9.3229s+0.0019s)
3222^3941-3941^3222 is 3-PRP! (9.3438s+0.0020s)
3222^3941-3941^3222 is 5-PRP! (9.2817s+0.0019s)
3222^3941-3941^3222 is 7-PRP! (9.2370s+0.0020s)
3222^3941-3941^3222 is 11-PRP! (9.2338s+0.0023s)

Primality testing 3222^3941-3941^3222 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 7
Running N+1 test using discriminant 13, base 1+sqrt(13)
Calling N+1 BLS with factored part 0.06% and helper 0.01% (0.20% proof)
3222^3941-3941^3222 is Fermat and Lucas PRP! (43.5195s+0.0034s)

To be completed...