Found with PFGW Version 3.7.5

1042^14777+14777^1042 is 2-PRP! (74.9913s+0.0034s)
1042^14777+14777^1042 is 3-PRP! (83.2302s+0.0038s)
1042^14777+14777^1042 is 5-PRP! (88.5718s+0.0028s)
1042^14777+14777^1042 is 7-PRP! (88.1310s+0.0040s)
1042^14777+14777^1042 is 11-PRP! (93.3127s+0.0035s)

Primality testing 1042^14777+14777^1042 [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 discriminant 13, base 1+sqrt(13)
Calling N+1 BLS with factored part 0.01% and helper 0.01% (0.05% proof)
1042^14777+14777^1042 is Fermat and Lucas PRP! (414.5091s+0.0036s)

To be completed...