Found with PFGW Version 3.8.0

581^20068+20068^581 is 2-PRP! (58.9542s+0.0063s)
581^20068+20068^581 is 3-PRP! (58.9376s+0.0064s)
581^20068+20068^581 is 5-PRP! (58.8677s+0.0082s)
581^20068+20068^581 is 7-PRP! (58.9191s+0.0069s)
581^20068+20068^581 is 11-PRP! (58.9462s+0.0075s)

Primality testing 581^20068+20068^581 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 7, base 1+sqrt(7)
Calling N+1 BLS with factored part 0.02% and helper 0.01% (0.06% proof)
581^20068+20068^581 is Fermat and Lucas PRP! (345.4461s+0.0073s)

To be completed...