Found with PFGW Version 3.7.5

96^31913-95 is 2-PRP! (24.1758s+0.0017s)
96^31913-95 is 3-PRP! (24.0852s+0.0020s)
96^31913-95 is 5-PRP! (24.1199s+0.0019s)
96^31913-95 is 7-PRP! (24.0753s+0.0021s)
96^31913-95 is 11-PRP! (24.4546s+0.0021s)

Primality testing 96^31913-95 [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 base 43
Running N+1 test using discriminant 53, base 3+sqrt(53)
Calling N-1 BLS with factored part 0.06% and helper 0.02% (0.19% proof)
96^31913-95 is Fermat and Lucas PRP! (223.5777s+0.0019s)

To be completed...