Checks
The Luhn key tells you a number is well formed. Not that it exists.
Everything runs in your browser. Nothing is sent.
Public test numbers:
Luhn is a typing check. It catches every single digit error and almost every swap of two neighbouring digits, except 09 into 90. A correct key says nothing about whether the card exists, whether it is active, or who issued it: the test numbers above belong to nobody.
Do not paste a real number here. Nothing leaves this page, but a card number has no business sitting in a clipboard, or in a browser history.
The same check runs everywhere, from the terminal keypad to the issuer. The rest is told in the episodes.