Found with PFGW Version 3.6.0

3499^6498-6498^3499 is 2-PRP! (21.9977s+0.0024s)
3499^6498-6498^3499 is 3-PRP! (22.4484s+0.0023s)
3499^6498-6498^3499 is 5-PRP! (22.5669s+0.0023s)
3499^6498-6498^3499 is 7-PRP! (22.4183s+0.0034s)
3499^6498-6498^3499 is 11-PRP! (22.6272s+0.0027s)

Primality testing 3499^6498-6498^3499 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 7
Running N+1 test using discriminant 23, base 3+sqrt(23)
Calling N+1 BLS with factored part 0.05% and helper 0.03% (0.19% proof)
3499^6498-6498^3499 is Fermat and Lucas PRP! (109.5817s+0.0025s)

To be completed...