Found with PFGW Version 3.7.5

823^7530-7530^823 is 2-PRP! (20.0764s+0.0039s)
823^7530-7530^823 is 3-PRP! (19.8387s+0.0039s)
823^7530-7530^823 is 5-PRP! (19.6838s+0.0033s)
823^7530-7530^823 is 7-PRP! (19.6661s+0.0022s)
823^7530-7530^823 is 11-PRP! (19.5618s+0.0021s)

Primality testing 823^7530-7530^823 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 7
Running N-1 test using base 13
Running N+1 test using discriminant 29, base 1+sqrt(29)
Calling N+1 BLS with factored part 0.05% and helper 0.03% (0.18% proof)
823^7530-7530^823 is Fermat and Lucas PRP! (120.3210s+0.0041s)

To be completed...