Other than because it’s “different”, why can’t you use a plugin?
Yes, I have mentioned that in the title. It is definitely a WP website. I got that from the links but I am not sure about the Generator thingy… Shall I include the link of that generator post? It would be easy to understand rather than discussing it vaguely?
I haven’t added it yet because I thought my post might be considered as spam since it is a new account.
Just put it in the back-end of your theme. Also, you’ll need some additional HTML + CSS to make the front-end. This won’t be possible using any plugin or WP custom widget. You need to code this on your own.
I did a quick internet search for fake credit card number generator Wordpress plugins. Nothing really stands out. You will need to write your own plugin for Wordpress or add code manually to the theme to do so.