Found with PFGW Version 3.7.5

3897^8542-8542^3897 is 2-PRP! (16.1653s+0.0015s)
3897^8542-8542^3897 is 3-PRP! (16.1220s+0.0014s)
3897^8542-8542^3897 is 5-PRP! (16.1550s+0.0013s)
3897^8542-8542^3897 is 7-PRP! (16.0802s+0.0013s)
3897^8542-8542^3897 is 11-PRP! (16.1539s+0.0014s)

Primality testing 3897^8542-8542^3897 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 13, base 1+sqrt(13)
Calling N+1 BLS with factored part 0.03% and helper 0.01% (0.09% proof)
3897^8542-8542^3897 is Fermat and Lucas PRP! (81.0981s+0.0022s)

To be completed...