Permutations and Combinations?

The total number of possible numbers is 10^16. The number of valid numbers are 100 million which is 10^8. The probability is 10^8 / 10^16 = 10^-8. That is a millionth of one percent.

engineer, I studied factoring in college, but forgot the concept. Can you provide a simple summary of how it works? It might jiggle my brains. Thanks in advance. Also studied statistics, but have never used it during my working career.

I could but this website will do a better job.

Thanks a million! We also studied differential calculus to use in inventory control to maximize efficiency. Great tools that many businesses fails to use. When I worked forFlorsheim Shoe Company, I got promoted to Audit Manager, but didn’t need to use it, because the store manager usually knew what was in demand, and each store had a district manager. When I was a field auditor, I covered the seven western states, and made my own schedule to audit each store twice a year. Was on a generous expense account, and stayed at some of the top hotels. Also bought Florsheims at cost. A huge change from our youth, when we could only afford Gallen Kamp Shoes.

Engineer is correct. But he didn't define the difference between a valid credit card number, and an invalid one. A valid Credit card number will always pass the Luhn algorithm.

This is a mathematical test that is designed to prevent typos. If you invert two numbers while typing in your credit card number, the resulting number will be invalid and whatever system you are using can detect it right away without having to check with a server.

That is the reason that just picking a random credit card number probably isn't valid.

https://en.wikipedia.org/wiki/Luhn_algorithm

Thanks for sharing that info. It's the first time I heard of that; Luhn algorithm.

I found out about it when someone sent a phishing email to my group of software engineers. We decided to have some fun with it. We went to the villain's webpage so we could see the code. The webpage asked for a credit card number. We typed in random numbers. The page rejected it.

We then generated a "valid" credit card number... at random. And viola, the crooks gave us access to their page.

I won't say what we did next

Since the Equifax bust, it’s too late.