Found with PFGW Version 3.4.6

1981^3042-3042^1981 is 2-PRP! (14.1178s+0.0055s)
1981^3042-3042^1981 is 3-PRP! (13.6117s+0.0030s)
1981^3042-3042^1981 is 5-PRP! (17.7795s+0.0013s)
1981^3042-3042^1981 is 7-PRP! (13.8034s+0.0012s)
1981^3042-3042^1981 is 11-PRP! (14.4001s+0.0013s)

Primality testing 1981^3042-3042^1981 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 7
Running N+1 test using discriminant 17, base 6+sqrt(17)
Calling N-1 BLS with factored part 0.18% and helper 0.05% (0.61% proof)
1981^3042-3042^1981 is Fermat and Lucas PRP! (81.8087s+0.0124s)

To be completed...