Found with PFGW Version 3.8.0

672^12851-12851^672 is 2-PRP! (24.5325s+0.0039s)
672^12851-12851^672 is 3-PRP! (24.0839s+0.0040s)
672^12851-12851^672 is 5-PRP! (24.0019s+0.0039s)
672^12851-12851^672 is 7-PRP! (23.9544s+0.0048s)
672^12851-12851^672 is 11-PRP! (23.8822s+0.0100s)

Primality testing 672^12851-12851^672 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 11, base 2+sqrt(11)
Calling N+1 BLS with factored part 0.04% and helper 0.00% (0.13% proof)
672^12851-12851^672 is Fermat and Lucas PRP! (118.1677s+0.0081s)

To be completed...