Found with PFGW Version 3.6.0

2167^4566-4566^2167 is 2-PRP! (10.3185s+0.0022s)
2167^4566-4566^2167 is 3-PRP! (10.2739s+0.0019s)
2167^4566-4566^2167 is 5-PRP! (10.2721s+0.0024s)
2167^4566-4566^2167 is 7-PRP! (10.1841s+0.0022s)
2167^4566-4566^2167 is 11-PRP! (10.2660s+0.0035s)

Primality testing 2167^4566-4566^2167 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 11, base 1+sqrt(11)
Calling N-1 BLS with factored part 0.05% and helper 0.05% (0.22% proof)
2167^4566-4566^2167 is Fermat and Lucas PRP! (48.9265s+0.0021s)

To be completed...