Found with PFGW Version 3.8.0

266^13777-13777^266 is 2-PRP! (22.3168s+0.0040s)
266^13777-13777^266 is 3-PRP! (21.8597s+0.0041s)
266^13777-13777^266 is 5-PRP! (21.9774s+0.0041s)
266^13777-13777^266 is 7-PRP! (21.9020s+0.0047s)
266^13777-13777^266 is 11-PRP! (21.9283s+0.0044s)

Primality testing 266^13777-13777^266 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 23, base 1+sqrt(23)
Calling N+1 BLS with factored part 0.01% and helper 0.00% (0.03% proof)
266^13777-13777^266 is Fermat and Lucas PRP! (107.9386s+0.0041s)

To be completed...