Found with PFGW Version 3.7.5

3667^8222-8222^3667 is 2-PRP! (27.3250s+0.0015s)
3667^8222-8222^3667 is 3-PRP! (26.2388s+0.0012s)
3667^8222-8222^3667 is 5-PRP! (26.2479s+0.0016s)
3667^8222-8222^3667 is 7-PRP! (26.5413s+0.0014s)
3667^8222-8222^3667 is 11-PRP! (27.1580s+0.0012s)

Primality testing 3667^8222-8222^3667 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 11, base 11+sqrt(11)
Calling N-1 BLS with factored part 0.01% and helper 0.00% (0.04% proof)
3667^8222-8222^3667 is Fermat and Lucas PRP! (143.2496s+0.0146s)

To be completed...