I don't believe we are that close to running out though, are we?

Using the number scheme, this person calculated^1 that (assuming Amex starts issuing 16 digit cards) there would be 3*10^14 + 10^11 or 4.001e+14 possible combinations.

[1]: https://www.reddit.com/r/theydidthemath/comments/3wj8eb/requ...