Found with PFGW Version 3.7.5

359^20992+20992^359 is 2-PRP! (131.3213s+0.0056s)
359^20992+20992^359 is 3-PRP! (133.9119s+0.0061s)
359^20992+20992^359 is 5-PRP! (127.4331s+0.0054s)
359^20992+20992^359 is 7-PRP! (135.4128s+0.0062s)
359^20992+20992^359 is 11-PRP! (125.7650s+0.0077s)

Primality testing 359^20992+20992^359 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 11, base 7+sqrt(11)
Calling N-1 BLS with factored part 0.03% and helper 0.00% (0.09% proof)
359^20992+20992^359 is Fermat and Lucas PRP! (666.3667s+0.0045s)

To be completed...