Found with PFGW Version 3.7.5

1717^5166-5166^1717 is 2-PRP! (9.2631s+0.0017s)
1717^5166-5166^1717 is 3-PRP! (9.6019s+0.0018s)
1717^5166-5166^1717 is 5-PRP! (9.0352s+0.0023s)
1717^5166-5166^1717 is 7-PRP! (9.0186s+0.0017s)
1717^5166-5166^1717 is 11-PRP! (9.9649s+0.0026s)

Primality testing 1717^5166-5166^1717 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 11, base 1+sqrt(11)
Calling N-1 BLS with factored part 0.07% and helper 0.00% (0.20% proof)
1717^5166-5166^1717 is Fermat and Lucas PRP! (44.9872s+0.0017s)

To be completed...