Found with PFGW Version 3.7.5

1281^7822-7822^1281 is 2-PRP! (27.2898s+0.0022s)
1281^7822-7822^1281 is 3-PRP! (25.0358s+0.0024s)
1281^7822-7822^1281 is 5-PRP! (26.6006s+0.0022s)
1281^7822-7822^1281 is 7-PRP! (17.6763s+0.0017s)
1281^7822-7822^1281 is 11-PRP! (19.2799s+0.0016s)

Primality testing 1281^7822-7822^1281 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 11, base 7+sqrt(11)
Calling N-1 BLS with factored part 0.04% and helper 0.04% (0.17% proof)
1281^7822-7822^1281 is Fermat and Lucas PRP! (122.1321s+0.0042s)

To be completed...