Found with PFGW Version 3.7.5

18565^30002-30002^18565 is 2-PRP! (371.2074s+0.0058s)
18565^30002-30002^18565 is 3-PRP! (370.1628s+0.0058s)
18565^30002-30002^18565 is 5-PRP! (362.6696s+0.0056s)
18565^30002-30002^18565 is 7-PRP! (357.9120s+0.0055s)
18565^30002-30002^18565 is 11-PRP! (358.0295s+0.0055s)

Primality testing 18565^30002-30002^18565 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 11, base 1+sqrt(11)
Calling N-1 BLS with factored part 0.01% and helper 0.01% (0.03% proof)
18565^30002-30002^18565 is Fermat and Lucas PRP! (1797.5266s+0.0067s)

To be completed...