The number 3222223 is a depression prime.
PFGW Version 1.2.0 for Windows [FFT v23.8]
Primality testing 10^16625+3222223 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 11, base 3+sqrt(11)
Running N+1 test using discriminant 11, base 4+sqrt(11)
10^16625+3222223 is Fermat and Lucas PRP!
To be completed...