Found with PFGW Version 3.7.5

7572^10573-10573^7572 is 2-PRP! (34.7306s+0.0019s)
7572^10573-10573^7572 is 3-PRP! (35.5348s+0.0017s)
7572^10573-10573^7572 is 5-PRP! (35.8748s+0.0019s)
7572^10573-10573^7572 is 7-PRP! (36.1271s+0.0018s)
7572^10573-10573^7572 is 11-PRP! (36.3068s+0.0020s)

Primality testing 7572^10573-10573^7572 [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 0.02% and helper 0.01% (0.07% proof)
7572^10573-10573^7572 is Fermat and Lucas PRP! (174.5313s+0.0030s)

To be completed...