Found with PFGW Version 3.8.0

5970^12797-12797^5970 is 2-PRP! (44.2029s+0.0079s)
5970^12797-12797^5970 is 3-PRP! (45.1426s+0.0147s)
5970^12797-12797^5970 is 5-PRP! (45.1322s+0.0082s)
5970^12797-12797^5970 is 7-PRP! (43.5042s+0.0078s)
5970^12797-12797^5970 is 11-PRP! (44.3281s+0.0084s)

Primality testing 5970^12797-12797^5970 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 11
Running N+1 test using discriminant 19, base 1+sqrt(19)
Calling N+1 BLS with factored part 0.03% and helper 0.02% (0.10% proof)
5970^12797-12797^5970 is Fermat and Lucas PRP! (256.4270s+0.0084s)

To be completed...