Pick an irrational number, like pi.
How many valid credit cards are there in the first n digits of that number?
Pick another irrational number, like e.
How many valid credit cards are there in the first n digits of that number? More than the first number? Less?
Why?
Here's a silly little afternoon project to try to answer all of the above questions. Except maybe for Why. That may be unanswerable.
This is a PHP script designed to take a list of irrational numbers (stored externally and statically) and march through their digits counting up the credit card numbers. As many rules as possible of client-side credit card validation apply (luhn checks and card-vendor-specific formats). Put another way, the "matches" are all valid-looking. While they could certainly be used for, say, testing a credit card API, there is no gaurantee (or bank-side verification) that these are legitimate credit cards.
This is not a project to try to mine credit card data, either. Did you read Contact by Carl Sagan? The movie doesn't count; you'd have to read the book. The big payoff/mystery at the end that never made it into the film - that's sort of along the same lines as this. Although this is a lot less cosmic-truthy and more just dinking around with random numbers.
That's pretty much it.
In their first 10,000 digits, the following irrationals have the following numbers of cards:
- pi - 215
- e - 237
- square root of 2 - 216
- square root of 3 - 220
- phi (the golden ratio) - 192
- gamma (Euler's constant) - 213
What does this mean? Hell if I know.
More Everything
More digits, more irrationals. Maybe more niche card types.
Card Type Distribution
The script is presently smart enough to know which type of card it found (Visa/Amex/Discover/etc). Maybe it would be cool to see the distribution of card types across the different irrationals. Maybe phi is loaded up with Mastercards for some reason.
Various Values of n
At 10,000 digits all but phi and e are within a few matches of each other in terms of volume. Does the number of matches scale linearly with the number of digits and phi just goes at a slower rate than the others? Maybe for some values of n digits the distribution is a lot more varied, like a horse race where the leader is constantly switching. This is good fodder for visualization down the line.
Math.