Found with PFGW Version 3.7.5

10236^10445-10445^10236 is 2-PRP! (35.5118s+0.0032s)
10236^10445-10445^10236 is 3-PRP! (35.8992s+0.0028s)
10236^10445-10445^10236 is 5-PRP! (35.6341s+0.0035s)
10236^10445-10445^10236 is 7-PRP! (35.1671s+0.0031s)
10236^10445-10445^10236 is 11-PRP! (35.8160s+0.0028s)

Primality testing 10236^10445-10445^10236 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 11
Running N+1 test using discriminant 23, base 2+sqrt(23)
Calling N+1 BLS with factored part 0.01% and helper 0.01% (0.06% proof)
10236^10445-10445^10236 is Fermat and Lucas PRP! (196.7209s+0.0040s)

To be completed...