Found with PFGW Version 3.7.5

4569^12448+12448^4569 is 2-PRP! (96.0170s+0.0058s)
4569^12448+12448^4569 is 3-PRP! (96.3459s+0.0056s)
4569^12448+12448^4569 is 5-PRP! (95.0330s+0.0053s)
4569^12448+12448^4569 is 7-PRP! (95.4810s+0.0060s)
4569^12448+12448^4569 is 11-PRP! (87.4321s+0.0050s)

Primality testing 4569^12448+12448^4569 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 7
Running N+1 test using discriminant 17, base 6+sqrt(17)
Calling N-1 BLS with factored part 0.01% and helper 0.01% (0.05% proof)
4569^12448+12448^4569 is Fermat and Lucas PRP! (467.5609s+0.0064s)

To be completed...