Found with PFGW Version 3.7.5

1277^5190-5190^1277 is 2-PRP! (9.7358s+0.0022s)
1277^5190-5190^1277 is 3-PRP! (9.1086s+0.0020s)
1277^5190-5190^1277 is 5-PRP! (8.5596s+0.0022s)
1277^5190-5190^1277 is 7-PRP! (8.7287s+0.0025s)
1277^5190-5190^1277 is 11-PRP! (8.3409s+0.0020s)

Primality testing 1277^5190-5190^1277 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 7
Running N+1 test using discriminant 13, base 8+sqrt(13)
Calling N-1 BLS with factored part 0.03% and helper 0.01% (0.10% proof)
1277^5190-5190^1277 is Fermat and Lucas PRP! (42.7809s+0.0045s)

To be completed...