Found with PFGW Version 3.7.5

3500^5689-5689^3500 is 2-PRP! (15.1618s+0.0019s)
3500^5689-5689^3500 is 3-PRP! (14.5831s+0.0020s)
3500^5689-5689^3500 is 5-PRP! (15.4277s+0.0025s)
3500^5689-5689^3500 is 7-PRP! (14.9281s+0.0025s)
3500^5689-5689^3500 is 11-PRP! (15.0530s+0.0018s)

Primality testing 3500^5689-5689^3500 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 11, base 1+sqrt(11)
Calling N-1 BLS with factored part 0.02% and helper 0.02% (0.09% proof)
3500^5689-5689^3500 is Fermat and Lucas PRP! (73.8626s+0.0044s)

To be completed...