Found with PFGW Version 3.8.0

10530^13381-13381^10530 is 2-PRP! (55.2459s+0.0091s)
10530^13381-13381^10530 is 3-PRP! (57.3573s+0.0098s)
10530^13381-13381^10530 is 5-PRP! (55.3117s+0.0096s)
10530^13381-13381^10530 is 7-PRP! (57.3820s+0.0115s)
10530^13381-13381^10530 is 11-PRP! (58.3802s+0.0113s)

Primality testing 10530^13381-13381^10530 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 7
Running N-1 test using base 17
Running N+1 test using discriminant 29, base 2+sqrt(29)
Calling N+1 BLS with factored part 0.02% and helper 0.01% (0.06% proof)
10530^13381-13381^10530 is Fermat and Lucas PRP! (336.2794s+0.0147s)

To be completed...