Found with PFGW Version 3.7.5

384^5173-5173^384 is 2-PRP! (5.8314s+0.0013s)
384^5173-5173^384 is 3-PRP! (6.2237s+0.0013s)
384^5173-5173^384 is 5-PRP! (5.8892s+0.0016s)
384^5173-5173^384 is 7-PRP! (5.8828s+0.0014s)
384^5173-5173^384 is 11-PRP! (6.4866s+0.0015s)

Primality testing 384^5173-5173^384 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 13, base 1+sqrt(13)
Calling N+1 BLS with factored part 0.18% and helper 0.11% (0.65% proof)
384^5173-5173^384 is Fermat and Lucas PRP! (28.3371s+0.0012s)

To be completed...