Found with PFGW Version 3.7.5

7220^8381-8381^7220 is 2-PRP! (19.4039s+0.0035s)
7220^8381-8381^7220 is 3-PRP! (18.9887s+0.0018s)
7220^8381-8381^7220 is 5-PRP! (18.8165s+0.0035s)
7220^8381-8381^7220 is 7-PRP! (19.0733s+0.0017s)
7220^8381-8381^7220 is 11-PRP! (18.9653s+0.0018s)

Primality testing 7220^8381-8381^7220 [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 0.03% and helper 0.03% (0.12% proof)
7220^8381-8381^7220 is Fermat and Lucas PRP! (122.3883s+0.0029s)

To be completed...