Found with PFGW Version 3.7.5

9734^10355-10355^9734 is 2-PRP! (35.6276s+0.0022s)
9734^10355-10355^9734 is 3-PRP! (35.6558s+0.0022s)
9734^10355-10355^9734 is 5-PRP! (35.8784s+0.0020s)
9734^10355-10355^9734 is 7-PRP! (36.0270s+0.0021s)
9734^10355-10355^9734 is 11-PRP! (35.6007s+0.0022s)

Primality testing 9734^10355-10355^9734 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 13, base 2+sqrt(13)
Calling N+1 BLS with factored part 0.03% and helper 0.02% (0.12% proof)
9734^10355-10355^9734 is Fermat and Lucas PRP! (178.8038s+0.0029s)

To be completed...