Found with PFGW Version 3.8.0

423^30634+30634^423 is 2-PRP! (125.0974s+0.0087s)
423^30634+30634^423 is 3-PRP! (123.5599s+0.0061s)
423^30634+30634^423 is 5-PRP! (128.7251s+0.0090s)
423^30634+30634^423 is 7-PRP! (125.6545s+0.0088s)
423^30634+30634^423 is 11-PRP! (124.8671s+0.0065s)

Primality testing 423^30634+30634^423 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 11, base 1+sqrt(11)
Calling N-1 BLS with factored part 0.01% and helper 0.00% (0.02% proof)
423^30634+30634^423 is Fermat and Lucas PRP! (723.1180s+0.0102s)

To be completed...