Found with PFGW Version 3.7.5

6517^7920-7920^6517 is 2-PRP! (33.4504s+0.0047s)
6517^7920-7920^6517 is 3-PRP! (37.2897s+0.0045s)
6517^7920-7920^6517 is 5-PRP! (30.8019s+0.0026s)
6517^7920-7920^6517 is 7-PRP! (30.4632s+0.0026s)
6517^7920-7920^6517 is 11-PRP! (25.5008s+0.0023s)

Primality testing 6517^7920-7920^6517 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 13
Running N+1 test using discriminant 19, base 14+sqrt(19)
Calling N-1 BLS with factored part 0.04% and helper 0.02% (0.15% proof)
6517^7920-7920^6517 is Fermat and Lucas PRP! (178.1589s+0.0058s)

To be completed...