Found with PFGW Version 3.5.2

1299^3508-3508^1299 is 2-PRP! (21.7318s+0.0045s)
1299^3508-3508^1299 is 3-PRP! (24.6251s+0.0048s)
1299^3508-3508^1299 is 5-PRP! (19.8789s+0.0048s)
1299^3508-3508^1299 is 7-PRP! (21.9408s+0.0056s)
1299^3508-3508^1299 is 11-PRP! (25.4731s+0.0062s)

Primality testing 1299^3508-3508^1299 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 7, base 1+sqrt(7)
Calling N+1 BLS with factored part 0.07% and helper 0.01% (0.21% proof)
1299^3508-3508^1299 is Fermat and Lucas PRP! (131.9276s+0.0141s)

To be completed...