Found with PFGW Version 3.7.5

384^8185-8185^384 is 2-PRP! (19.5233s+0.0028s)
384^8185-8185^384 is 3-PRP! (19.8453s+0.0029s)
384^8185-8185^384 is 5-PRP! (19.2663s+0.0023s)
384^8185-8185^384 is 7-PRP! (19.2114s+0.0027s)
384^8185-8185^384 is 11-PRP! (19.6523s+0.0026s)

Primality testing 384^8185-8185^384 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 11
Running N+1 test using discriminant 17, base 1+sqrt(17)
Calling N+1 BLS with factored part 0.09% and helper 0.00% (0.28% proof)
384^8185-8185^384 is Fermat and Lucas PRP! (97.2400s+0.0037s)

To be completed...