Found with PFGW Version 3.8.0

4243^11126-11126^4243 is 2-PRP! (34.1247s+0.0062s)
4243^11126-11126^4243 is 3-PRP! (35.8672s+0.0103s)
4243^11126-11126^4243 is 5-PRP! (34.4344s+0.0064s)
4243^11126-11126^4243 is 7-PRP! (34.9216s+0.0078s)
4243^11126-11126^4243 is 11-PRP! (34.0513s+0.0065s)

Primality testing 4243^11126-11126^4243 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 7, base 1+sqrt(7)
Calling N-1 BLS with factored part 0.03% and helper 0.00% (0.09% proof)
4243^11126-11126^4243 is Fermat and Lucas PRP! (167.1931s+0.0078s)

To be completed...