Found with PFGW Version 3.6.0

1250^3877-3877^1250 is 2-PRP! (5.3696s+0.0018s)
1250^3877-3877^1250 is 3-PRP! (5.6645s+0.0021s)
1250^3877-3877^1250 is 5-PRP! (5.7426s+0.0022s)
1250^3877-3877^1250 is 7-PRP! (6.1205s+0.0020s)
1250^3877-3877^1250 is 11-PRP! (6.1750s+0.0032s)

Primality testing 1250^3877-3877^1250 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 11, base 1+sqrt(11)
Calling N-1 BLS with factored part 0.09% and helper 0.08% (0.34% proof)
1250^3877-3877^1250 is Fermat and Lucas PRP! (27.8865s+0.0033s)

To be completed...