Found with PFGW Version 3.6.0

835^4776-4776^835 is 2-PRP! (9.8840s+0.0017s)
835^4776-4776^835 is 3-PRP! (9.6587s+0.0019s)
835^4776-4776^835 is 5-PRP! (9.5809s+0.0025s)
835^4776-4776^835 is 7-PRP! (9.6404s+0.0019s)
835^4776-4776^835 is 11-PRP! (9.5115s+0.0019s)

Primality testing 835^4776-4776^835 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 7
Running N+1 test using discriminant 13, base 13+sqrt(13)
Calling N-1 BLS with factored part 0.08% and helper 0.03% (0.27% proof)
835^4776-4776^835 is Fermat and Lucas PRP! (43.6819s+0.0017s)

To be completed...