Found with PFGW Version 3.8.0

7353^13430-13430^7353 is 2-PRP! (48.0307s+0.0108s)
7353^13430-13430^7353 is 3-PRP! (48.0999s+0.0103s)
7353^13430-13430^7353 is 5-PRP! (48.1919s+0.0109s)
7353^13430-13430^7353 is 7-PRP! (47.9752s+0.0102s)
7353^13430-13430^7353 is 11-PRP! (48.0834s+0.0104s)

Primality testing 7353^13430-13430^7353 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 11
Running N-1 test using base 13
Running N+1 test using discriminant 19, base 9+sqrt(19)
Calling N+1 BLS with factored part 0.02% and helper 0.01% (0.07% proof)
7353^13430-13430^7353 is Fermat and Lucas PRP! (365.0183s+0.0422s)

To be completed...