However, some of the wording seems a little vague to me. It says "they are completely fake" and calls them "fake credit card numbers," but I do not see any mention of (what seems to me) the inevitable possibility that the algorithm might pop out a legitimate number. I have no idea what are the odds of that happening (possibly very low), but if it's possible, can you really call them "fake"?
It's somewhat unlikely that this tool will generate many "real" account numbers, as the Bank Identification Number field is being randomly generated as well. These account numbers only satisfy the Luhn check for validity.
You might find these links interesting, they explain credit card data in depth:
http://www.dirigodev.com/blog/anatomy-of-a-credit-card-numbe...
http://blog.opensecurityresearch.com/2012/02/deconstructing-...
As stated there (although as you said, poorly worded), the other use case by "normals" is for things like finding out how much it would cost to ship something from amazon before you actually want to buy etc.
Thanks for the feedback!
That's because the format of the credit card number is well known[1] and conforms to an ISO standard[2]. Numbers generated using publicly known issuer identifiers can then (usually) be checked for potential validity by running it through a standard checksum called the Luhn algorithm.[3] The Wikipedia article for the algorithm even helpfully provides a working Python script to do the work for you.
This is all well known stuff, and I seem to recall there being a joke file of "hacked" credit card numbers in the late 90s which I believe was just a list of numbers generated this way.
[1] https://en.wikipedia.org/wiki/Bank_card_number
[2] http://www.iso.org/iso/iso_catalogue/catalogue_tc/catalogue_...