Found with PFGW Version 3.6.0

1284^3877-3877^1284 is 2-PRP! (5.4187s+0.0018s)
1284^3877-3877^1284 is 3-PRP! (5.7133s+0.0017s)
1284^3877-3877^1284 is 5-PRP! (5.7847s+0.0034s)
1284^3877-3877^1284 is 7-PRP! (6.0655s+0.0021s)
1284^3877-3877^1284 is 11-PRP! (5.8663s+0.0021s)

Primality testing 1284^3877-3877^1284 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 11, base 3+sqrt(11)
Calling N-1 BLS with factored part 0.06% and helper 0.06% (0.24% proof)
1284^3877-3877^1284 is Fermat and Lucas PRP! (27.8433s+0.0035s)

To be completed...