Found with PFGW Version 3.4.8

621^6034-6034^621 is 2-PRP! (34.4682s+0.0360s)
621^6034-6034^621 is 3-PRP! (59.8738s+0.0172s)
621^6034-6034^621 is 5-PRP! (38.5210s+0.0179s)
621^6034-6034^621 is 7-PRP! (60.8682s+0.0057s)
621^6034-6034^621 is 11-PRP! (65.6779s+0.0053s)

Primality testing 621^6034-6034^621 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 13, base 1+sqrt(13)
Calling N+1 BLS with factored part 0.01% and helper 0.01% (0.04% proof)
621^6034-6034^621 is Fermat and Lucas PRP! (346.0806s+0.0155s)

To be completed...