Found with PFGW Version 3.8.0

6576^12565-12565^6576 is 2-PRP! (42.8548s+0.0056s)
6576^12565-12565^6576 is 3-PRP! (42.8483s+0.0107s)
6576^12565-12565^6576 is 5-PRP! (42.8302s+0.0070s)
6576^12565-12565^6576 is 7-PRP! (44.0079s+0.0068s)
6576^12565-12565^6576 is 11-PRP! (43.1278s+0.0073s)

Primality testing 6576^12565-12565^6576 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 11
Running N+1 test using discriminant 17, base 1+sqrt(17)
Calling N+1 BLS with factored part 0.02% and helper 0.01% (0.07% proof)
6576^12565-12565^6576 is Fermat and Lucas PRP! (243.8243s+0.0078s)

To be completed...