Found with PFGW Version 3.6.0

3325^4404-4404^3325 is 2-PRP! (10.3937s+0.0027s)
3325^4404-4404^3325 is 3-PRP! (10.3471s+0.0026s)
3325^4404-4404^3325 is 5-PRP! (10.3272s+0.0038s)
3325^4404-4404^3325 is 7-PRP! (10.3445s+0.0024s)
3325^4404-4404^3325 is 11-PRP! (10.3454s+0.0021s)

Primality testing 3325^4404-4404^3325 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 7
Running N+1 test using discriminant 17, base 8+sqrt(17)
Calling N-1 BLS with factored part 0.12% and helper 0.06% (0.44% proof)
3325^4404-4404^3325 is Fermat and Lucas PRP! (50.3810s+0.0036s)

To be completed...