Found with PFGW Version 3.6.0

4329^4414-4414^4329 is 2-PRP! (10.8377s+0.0035s)
4329^4414-4414^4329 is 3-PRP! (10.8730s+0.0023s)
4329^4414-4414^4329 is 5-PRP! (10.8770s+0.0054s)
4329^4414-4414^4329 is 7-PRP! (10.8858s+0.0037s)
4329^4414-4414^4329 is 11-PRP! (10.8797s+0.0026s)

Primality testing 4329^4414-4414^4329 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 7, base 1+sqrt(7)
Calling N-1 BLS with factored part 0.07% and helper 0.07% (0.27% proof)
4329^4414-4414^4329 is Fermat and Lucas PRP! (52.0252s+0.0033s)

To be completed...