Found with PFGW Version 3.7.5

65^56567-64 is 2-PRP! (61.0965s+0.0043s)
65^56567-64 is 3-PRP! (60.8720s+0.0051s)
65^56567-64 is 5-PRP! (60.9480s+0.0047s)
65^56567-64 is 7-PRP! (60.8726s+0.0049s)
65^56567-64 is 11-PRP! (60.7547s+0.0051s)

Primality testing 65^56567-64 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 7
Running N+1 test using discriminant 17, base 14+sqrt(17)
Calling N+1 BLS with factored part 0.01% and helper 0.01% (0.02% proof)
65^56567-64 is Fermat and Lucas PRP! (499.9990s+0.0048s)

To be completed...