Found with PFGW Version 3.7.5

9035^12622+12622^9035 is 2-PRP! (47.1358s+0.0029s)
9035^12622+12622^9035 is 3-PRP! (46.7834s+0.0031s)
9035^12622+12622^9035 is 5-PRP! (46.5827s+0.0030s)
9035^12622+12622^9035 is 7-PRP! (46.4894s+0.0030s)
9035^12622+12622^9035 is 11-PRP! (46.5083s+0.0030s)

Primality testing 9035^12622+12622^9035 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 7, base 1+sqrt(7)
Calling N-1 BLS with factored part 0.02% and helper 0.01% (0.08% proof)
9035^12622+12622^9035 is Fermat and Lucas PRP! (271.2286s+0.0031s)

To be completed...