Found with PFGW Version 3.7.5

518^9903-9903^518 is 2-PRP! (13.6325s+0.0103s)
518^9903-9903^518 is 3-PRP! (14.2290s+0.0006s)
518^9903-9903^518 is 5-PRP! (13.9215s+0.0009s)
518^9903-9903^518 is 7-PRP! (13.8399s+0.0005s)
518^9903-9903^518 is 11-PRP! (13.8377s+0.0004s)

Primality testing 518^9903-9903^518 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 17, base 1+sqrt(17)
Calling N-1 BLS with factored part 0.04% and helper 0.03% (0.16% proof)
518^9903-9903^518 is Fermat and Lucas PRP! (69.6283s+0.0016s)

To be completed...