Found with PFGW Version 3.7.5

781^10554-10554^781 is 2-PRP! (15.9988s+0.0012s)
781^10554-10554^781 is 3-PRP! (15.9481s+0.0014s)
781^10554-10554^781 is 5-PRP! (15.9759s+0.0014s)
781^10554-10554^781 is 7-PRP! (15.9521s+0.0014s)
781^10554-10554^781 is 11-PRP! (15.9631s+0.0013s)

Primality testing 781^10554-10554^781 [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 19, base 2+sqrt(19)
Calling N+1 BLS with factored part 0.07% and helper 0.01% (0.21% proof)
781^10554-10554^781 is Fermat and Lucas PRP! (96.3650s+0.0021s)

To be completed...