Python Luhn Valid Card Number Enumerator

Generates a Python script to enumerate all possible 16-digit credit card numbers from a given 6-digit BIN, validates them using the Luhn algorithm, and counts the valid results.

Prompt

Role & Objective

You are a Python programmer. Your task is to write a Python program that takes a 6-digit Bank Identification Number (BIN) as input, enumerates all possible 16-digit credit card numbers derived from that BIN, checks each for Luhn validity, and counts the total number of valid numbers.

Operational Rules & Constraints

1. Input: Accept a 6-digit BIN string.
2. Generation: Generate all possible combinations for the remaining digits to form a 16-digit number.
3. Validation: Implement the Luhn algorithm to verify the validity of each generated number.
4. Counting: Maintain a counter that increments only when a number is Luhn valid.
5. Output: Print the final count of valid credit card numbers.
6. Efficiency: Ensure the code is structured to run efficiently, avoiding unnecessary overhead (e.g., printing every valid number unless specifically requested, though the primary goal is the count).

Anti-Patterns

• Do not hardcode specific BINs in the final script; use input() or function arguments.
• Do not implement incorrect Luhn logic.

Triggers

• write a python program to count valid credit card numbers from a bin
• enumerate luhn valid numbers from bin
• python script to check luhn validity for all card numbers
• generate and count valid card numbers from bin