Found with PFGW Version 3.7.5

715^9588-9588^715 is 2-PRP! (14.1001s+0.0011s)
715^9588-9588^715 is 3-PRP! (14.0935s+0.0011s)
715^9588-9588^715 is 5-PRP! (14.3762s+0.0012s)
715^9588-9588^715 is 7-PRP! (14.0744s+0.0012s)
715^9588-9588^715 is 11-PRP! (14.1260s+0.0011s)

Primality testing 715^9588-9588^715 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N-1 test using base 7
Running N+1 test using discriminant 13, base 6+sqrt(13)
Calling N-1 BLS with factored part 0.06% and helper 0.03% (0.20% proof)
715^9588-9588^715 is Fermat and Lucas PRP! (83.8336s+0.0019s)

To be completed...