Found with PFGW Version 3.7.5

3122^8119-8119^3122 is 2-PRP! (28.3620s+0.0025s)
3122^8119-8119^3122 is 3-PRP! (31.2214s+0.0024s)
3122^8119-8119^3122 is 5-PRP! (34.9742s+0.0027s)
3122^8119-8119^3122 is 7-PRP! (33.1509s+0.0026s)
3122^8119-8119^3122 is 11-PRP! (35.9820s+0.0024s)

Primality testing 3122^8119-8119^3122 [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 0.05% and helper 0.01% (0.16% proof)
3122^8119-8119^3122 is Fermat and Lucas PRP! (176.5375s+0.0048s)

To be completed...