Found with PFGW Version 3.7.5

3505^5568-5568^3505 is 2-PRP! (14.1558s+0.0021s)
3505^5568-5568^3505 is 3-PRP! (13.4890s+0.0025s)
3505^5568-5568^3505 is 5-PRP! (13.9223s+0.0023s)
3505^5568-5568^3505 is 7-PRP! (13.7852s+0.0022s)
3505^5568-5568^3505 is 11-PRP! (15.4811s+0.0024s)

Primality testing 3505^5568-5568^3505 [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 0.06% and helper 0.05% (0.22% proof)
3505^5568-5568^3505 is Fermat and Lucas PRP! (74.1398s+0.0037s)

To be completed...