Found with PFGW Version 3.7.5

1370^7023-7023^1370 is 2-PRP! (16.2526s+0.0097s)
1370^7023-7023^1370 is 3-PRP! (16.9142s+0.0015s)
1370^7023-7023^1370 is 5-PRP! (19.8620s+0.0012s)
1370^7023-7023^1370 is 7-PRP! (15.7067s+0.0006s)
1370^7023-7023^1370 is 11-PRP! (16.1207s+0.0008s)

Primality testing 1370^7023-7023^1370 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 7
Running N+1 test using discriminant 19, base 1+sqrt(19)
Calling N+1 BLS with factored part 0.03% and helper 0.01% (0.09% proof)
1370^7023-7023^1370 is Fermat and Lucas PRP! (81.2418s+0.0017s)

To be completed...