Found with PFGW Version 3.6.0

1672^4395-4395^1672 is 2-PRP! (9.5015s+0.0019s)
1672^4395-4395^1672 is 3-PRP! (9.4603s+0.0018s)
1672^4395-4395^1672 is 5-PRP! (9.4539s+0.0018s)
1672^4395-4395^1672 is 7-PRP! (9.4132s+0.0018s)
1672^4395-4395^1672 is 11-PRP! (9.5070s+0.0017s)

Primality testing 1672^4395-4395^1672 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 23, base 1+sqrt(23)
Calling N+1 BLS with factored part 0.06% and helper 0.04% (0.22% proof)
1672^4395-4395^1672 is Fermat and Lucas PRP! (45.4123s+0.0020s)

To be completed...