Found with PFGW Version 3.8.0

18^34979-34979^18 is 2-PRP! (36.2091s+0.0033s)
18^34979-34979^18 is 3-PRP! (36.0408s+0.0041s)
18^34979-34979^18 is 5-PRP! (36.1046s+0.0095s)
18^34979-34979^18 is 7-PRP! (38.5288s+0.0040s)
18^34979-34979^18 is 11-PRP! (36.0477s+0.0037s)

Primality testing 18^34979-34979^18 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 7
Running N+1 test using discriminant 13, base 1+sqrt(13)
Calling N+1 BLS with factored part 0.02% and helper 0.01% (0.07% proof)
18^34979-34979^18 is Fermat and Lucas PRP! (185.5752s+0.0063s)

To be completed...