Found with PFGW Version 3.7.5

7172^8549-8549^7172 is 2-PRP! (21.9931s+0.0016s)
7172^8549-8549^7172 is 3-PRP! (21.3008s+0.0015s)
7172^8549-8549^7172 is 5-PRP! (21.7648s+0.0016s)
7172^8549-8549^7172 is 7-PRP! (21.2306s+0.0017s)
7172^8549-8549^7172 is 11-PRP! (21.4715s+0.0016s)

Primality testing 7172^8549-8549^7172 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 13, base 2+sqrt(13)
Calling N+1 BLS with factored part 0.06% and helper 0.02% (0.21% proof)
7172^8549-8549^7172 is Fermat and Lucas PRP! (105.8438s+0.0028s)

To be completed...