Found with PFGW Version 3.7.5

782^9713-9713^782 is 2-PRP! (14.9296s+0.0011s)
782^9713-9713^782 is 3-PRP! (14.9125s+0.0011s)
782^9713-9713^782 is 5-PRP! (15.2082s+0.0011s)
782^9713-9713^782 is 7-PRP! (15.2432s+0.0010s)
782^9713-9713^782 is 11-PRP! (14.6774s+0.0011s)

Primality testing 782^9713-9713^782 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 7, base 10+sqrt(7)
Calling N+1 BLS with factored part 0.03% and helper 0.02% (0.10% proof)
782^9713-9713^782 is Fermat and Lucas PRP! (73.5680s+0.0019s)

To be completed...