Found with PFGW Version 3.7.5

10190^10341-10341^10190 is 2-PRP! (35.7367s+0.0029s)
10190^10341-10341^10190 is 3-PRP! (35.8167s+0.0030s)
10190^10341-10341^10190 is 5-PRP! (36.5861s+0.0030s)
10190^10341-10341^10190 is 7-PRP! (36.2737s+0.0030s)
10190^10341-10341^10190 is 11-PRP! (35.6797s+0.0028s)

Primality testing 10190^10341-10341^10190 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 7
Running N+1 test using discriminant 13, base 1+sqrt(13)
Calling N+1 BLS with factored part 0.05% and helper 0.01% (0.15% proof)
10190^10341-10341^10190 is Fermat and Lucas PRP! (179.7283s+0.0031s)

To be completed...