Found with PFGW Version 3.6.0

786^4475-4475^786 is 2-PRP! (6.6350s+0.0018s)
786^4475-4475^786 is 3-PRP! (6.6260s+0.0021s)
786^4475-4475^786 is 5-PRP! (6.6884s+0.0021s)
786^4475-4475^786 is 7-PRP! (6.6049s+0.0021s)
786^4475-4475^786 is 11-PRP! (6.6160s+0.0040s)

Primality testing 786^4475-4475^786 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 11
Running N+1 test using discriminant 17, base 1+sqrt(17)
Calling N-1 BLS with factored part 0.06% and helper 0.01% (0.19% proof)
786^4475-4475^786 is Fermat and Lucas PRP! (37.4426s+0.0034s)

To be completed...