Found with PFGW Version 3.8.0

11172^11275-11275^11172 is 2-PRP! (39.1340s+0.0047s)
11172^11275-11275^11172 is 3-PRP! (38.7024s+0.0044s)
11172^11275-11275^11172 is 5-PRP! (38.8592s+0.0074s)
11172^11275-11275^11172 is 7-PRP! (38.9764s+0.0046s)
11172^11275-11275^11172 is 11-PRP! (38.8502s+0.0046s)

Primality testing 11172^11275-11275^11172 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 13, base 1+sqrt(13)
Calling N+1 BLS with factored part 0.02% and helper 0.00% (0.07% proof)
11172^11275-11275^11172 is Fermat and Lucas PRP! (192.3664s+0.0070s)

To be completed...