Found with PFGW Version 3.7.5

2315^6444-6444^2315 is 2-PRP! (16.8657s+0.0030s)
2315^6444-6444^2315 is 3-PRP! (17.2829s+0.0039s)
2315^6444-6444^2315 is 5-PRP! (18.7633s+0.0027s)
2315^6444-6444^2315 is 7-PRP! (21.1694s+0.0049s)
2315^6444-6444^2315 is 11-PRP! (18.0584s+0.0025s)

Primality testing 2315^6444-6444^2315 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 7
Running N-1 test using base 11
Running N+1 test using discriminant 17, base 2+sqrt(17)
Calling N-1 BLS with factored part 0.04% and helper 0.02% (0.14% proof)
2315^6444-6444^2315 is Fermat and Lucas PRP! (103.9748s+0.0035s)

To be completed...