Found with PFGW Version 3.7.5

354^6751-6751^354 is 2-PRP! (10.2193s+0.0098s)
354^6751-6751^354 is 3-PRP! (11.0162s+0.0005s)
354^6751-6751^354 is 5-PRP! (9.8662s+0.0008s)
354^6751-6751^354 is 7-PRP! (10.4727s+0.0006s)
354^6751-6751^354 is 11-PRP! (10.1080s+0.0005s)

Primality testing 354^6751-6751^354 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 11, base 2+sqrt(11)
Calling N+1 BLS with factored part 0.09% and helper 0.01% (0.28% proof)
354^6751-6751^354 is Fermat and Lucas PRP! (51.1116s+0.0024s)

To be completed...