Found with PFGW Version 3.7.5

717^7126-7126^717 is 2-PRP! (28.4838s+0.0062s)
717^7126-7126^717 is 3-PRP! (27.1446s+0.0052s)
717^7126-7126^717 is 5-PRP! (27.5435s+0.0075s)
717^7126-7126^717 is 7-PRP! (27.6374s+0.0071s)
717^7126-7126^717 is 11-PRP! (27.2704s+0.0067s)

Primality testing 717^7126-7126^717 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 13, base 1+sqrt(13)
Calling N+1 BLS with factored part 0.10% and helper 0.03% (0.32% proof)
717^7126-7126^717 is Fermat and Lucas PRP! (131.6097s+0.0065s)

To be completed...