Found with PFGW Version 3.6.0

355^4226-4226^355 is 2-PRP! (5.0335s+0.0018s)
355^4226-4226^355 is 3-PRP! (5.0604s+0.0018s)
355^4226-4226^355 is 5-PRP! (5.0318s+0.0017s)
355^4226-4226^355 is 7-PRP! (5.0193s+0.0018s)
355^4226-4226^355 is 11-PRP! (5.0167s+0.0016s)

Primality testing 355^4226-4226^355 [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 0.08% and helper 0.06% (0.31% proof)
355^4226-4226^355 is Fermat and Lucas PRP! (23.7431s+0.0018s)

To be completed...