Found with PFGW Version 3.7.5

3643^8384-8384^3643 is 2-PRP! (17.1144s+0.0014s)
3643^8384-8384^3643 is 3-PRP! (16.2993s+0.0013s)
3643^8384-8384^3643 is 5-PRP! (16.5168s+0.0014s)
3643^8384-8384^3643 is 7-PRP! (16.3461s+0.0013s)
3643^8384-8384^3643 is 11-PRP! (16.4551s+0.0013s)

Primality testing 3643^8384-8384^3643 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 11, base 1+sqrt(11)
Calling N+1 BLS with factored part 0.01% and helper 0.01% (0.05% proof)
3643^8384-8384^3643 is Fermat and Lucas PRP! (85.4984s+0.0024s)

To be completed...