Found with PFGW Version 3.6.0

3579^4138-4138^3579 is 2-PRP! (9.9348s+0.0023s)
3579^4138-4138^3579 is 3-PRP! (10.0184s+0.0023s)
3579^4138-4138^3579 is 5-PRP! (9.9862s+0.0038s)
3579^4138-4138^3579 is 7-PRP! (9.9899s+0.0021s)
3579^4138-4138^3579 is 11-PRP! (9.9256s+0.0022s)

Primality testing 3579^4138-4138^3579 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 19, base 2+sqrt(19)
Calling N+1 BLS with factored part 0.07% and helper 0.01% (0.24% proof)
3579^4138-4138^3579 is Fermat and Lucas PRP! (46.9542s+0.0022s)

To be completed...