Found with PFGW Version 3.7.5

1384^10635-10635^1384 is 2-PRP! (21.7956s+0.0020s)
1384^10635-10635^1384 is 3-PRP! (21.7976s+0.0022s)
1384^10635-10635^1384 is 5-PRP! (21.7567s+0.0018s)
1384^10635-10635^1384 is 7-PRP! (24.4545s+0.0025s)
1384^10635-10635^1384 is 11-PRP! (26.5507s+0.0029s)

Primality testing 1384^10635-10635^1384 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 7, base 8+sqrt(7)
Calling N+1 BLS with factored part 0.04% and helper 0.01% (0.12% proof)
1384^10635-10635^1384 is Fermat and Lucas PRP! (107.7786s+0.0021s)

To be completed...