Found with PFGW Version 3.7.5

1792^5823-5823^1792 is 2-PRP! (10.5214s+0.0013s)
1792^5823-5823^1792 is 3-PRP! (10.4220s+0.0016s)
1792^5823-5823^1792 is 5-PRP! (10.5325s+0.0015s)
1792^5823-5823^1792 is 7-PRP! (10.4848s+0.0012s)
1792^5823-5823^1792 is 11-PRP! (10.4441s+0.0014s)

Primality testing 1792^5823-5823^1792 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 11, base 2+sqrt(11)
Calling N-1 BLS with factored part 0.06% and helper 0.05% (0.25% proof)
1792^5823-5823^1792 is Fermat and Lucas PRP! (52.9979s+0.0033s)

To be completed...