Found with PFGW Version 3.6.0

518^4243-4243^518 is 2-PRP! (5.6933s+0.0031s)
518^4243-4243^518 is 3-PRP! (5.6881s+0.0018s)
518^4243-4243^518 is 5-PRP! (5.6821s+0.0018s)
518^4243-4243^518 is 7-PRP! (5.6753s+0.0018s)
518^4243-4243^518 is 11-PRP! (5.6854s+0.0017s)

Primality testing 518^4243-4243^518 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 17, base 1+sqrt(17)
Calling N+1 BLS with factored part 0.11% and helper 0.01% (0.34% proof)
518^4243-4243^518 is Fermat and Lucas PRP! (30.1170s+0.0035s)

To be completed...