Found with PFGW Version 3.8.0

10736^12645-12645^10736 is 2-PRP! (47.5697s+0.0139s)
10736^12645-12645^10736 is 3-PRP! (46.9872s+0.0083s)
10736^12645-12645^10736 is 5-PRP! (46.8995s+0.0078s)
10736^12645-12645^10736 is 7-PRP! (46.9646s+0.0081s)
10736^12645-12645^10736 is 11-PRP! (47.4663s+0.0082s)

Primality testing 10736^12645-12645^10736 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 7
Running N-1 test using base 13
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)
10736^12645-12645^10736 is Fermat and Lucas PRP! (324.8524s+0.0082s)

To be completed...