Found with PFGW Version 3.6.0

5834^9019-9019^5834 is 2-PRP! (53.8791s+0.0031s)
5834^9019-9019^5834 is 3-PRP! (53.9195s+0.0033s)
5834^9019-9019^5834 is 5-PRP! (54.0059s+0.0034s)
5834^9019-9019^5834 is 7-PRP! (53.9454s+0.0034s)
5834^9019-9019^5834 is 11-PRP! (53.9634s+0.0049s)

Primality testing 5834^9019-9019^5834 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 7, base 8+sqrt(7)
Calling N-1 BLS with factored part 0.02% and helper 0.02% (0.07% proof)
5834^9019-9019^5834 is Fermat and Lucas PRP! (258.1100s+0.0042s)

To be completed...