Found with PFGW Version 3.7.5

782^7601-7601^782 is 2-PRP! (16.8988s+0.0020s)
782^7601-7601^782 is 3-PRP! (17.1545s+0.0020s)
782^7601-7601^782 is 5-PRP! (14.5899s+0.0014s)
782^7601-7601^782 is 7-PRP! (17.3285s+0.0023s)
782^7601-7601^782 is 11-PRP! (19.5915s+0.0019s)

Primality testing 782^7601-7601^782 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N-1 test using base 7
Running N-1 test using base 11
Running N+1 test using discriminant 29, base 2+sqrt(29)
Calling N-1 BLS with factored part 0.07% and helper 0.01% (0.23% proof)
782^7601-7601^782 is Fermat and Lucas PRP! (138.3625s+0.0046s)

To be completed...