Question 1

Can the Luhn algorithm tell me if a card really exists?

Accepted Answer

No. Luhn only verifies that the last digit is consistent with the preceding digits, which catches typos but says nothing about whether the account exists, is valid or is frozen. Only the acquiring bank can do a real check.

Question 2

Why check the length and network too?

Accepted Answer

Each network uses different lengths and CVV digit counts — American Express is 15 digits with a 4-digit CVV, while most others are 16 digits with a 3-digit CVV. A number that satisfies the prefix, length and Luhn rules at once is at least plausibly well-formed.