Found with PFGW Version 3.6.0

445^4386-4386^445 is 2-PRP! (5.6815s+0.0030s)
445^4386-4386^445 is 3-PRP! (5.6778s+0.0019s)
445^4386-4386^445 is 5-PRP! (5.6794s+0.0017s)
445^4386-4386^445 is 7-PRP! (5.6906s+0.0018s)
445^4386-4386^445 is 11-PRP! (5.7053s+0.0017s)

Primality testing 445^4386-4386^445 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 11
Running N-1 test using base 19
Running N+1 test using discriminant 29, base 10+sqrt(29)
Calling N+1 BLS with factored part 0.12% and helper 0.05% (0.43% proof)
445^4386-4386^445 is Fermat and Lucas PRP! (39.3541s+0.0037s)

To be completed...