Found with PFGW Version 3.6.0

3209^4254-4254^3209 is 2-PRP! (10.1488s+0.0022s)
3209^4254-4254^3209 is 3-PRP! (10.0526s+0.0023s)
3209^4254-4254^3209 is 5-PRP! (10.0506s+0.0021s)
3209^4254-4254^3209 is 7-PRP! (10.0406s+0.0022s)
3209^4254-4254^3209 is 11-PRP! (10.0587s+0.0023s)

Primality testing 3209^4254-4254^3209 [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 0.03% (0.22% proof)
3209^4254-4254^3209 is Fermat and Lucas PRP! (47.4853s+0.0020s)

To be completed...