Found with PFGW Version 3.7.5

9534^10369-10369^9534 is 2-PRP! (35.6189s+0.0033s)
9534^10369-10369^9534 is 3-PRP! (35.6565s+0.0030s)
9534^10369-10369^9534 is 5-PRP! (36.4383s+0.0031s)
9534^10369-10369^9534 is 7-PRP! (35.9533s+0.0031s)
9534^10369-10369^9534 is 11-PRP! (35.6029s+0.0031s)

Primality testing 9534^10369-10369^9534 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 11, base 2+sqrt(11)
Calling N+1 BLS with factored part 0.03% and helper 0.00% (0.08% proof)
9534^10369-10369^9534 is Fermat and Lucas PRP! (176.1163s+0.0028s)

To be completed...