TITLE: How to understand and appreciate the prime number industry?
QUESTION [48 upvotes]: Why would I want to buy prime numbers? There is a website (found it!) selling a table of 400 digit primes for twenty dollars. Like an updated version of this. I have a layman's idea that prime numbers are important to cryptography but surely for this low a price, I don't think I can decrypt anything worthwhile. So what are the other uses that make prime numbers sellable at affordable home-user prices? 
Hypothetically, if I accidentally discovered a huge prime, would its importance depend just on how big it is? What would make it "rare" enough that it'll become my intellectual property to use commercially (number of hours a supercomputer takes to verify it? But what is the use?) This foundation gives prizes and for an amusing example, this guy claimed to have put his prime number for sale on ebay five years ago. 
I also discovered that there were illegal primes forbidden for commercial distribution, but I am looking for some mathematical reasoning why they are illegal.
Any pointers to online or other resources which explain why there's such a big deal behind the prime number industry would also be appreciated.

REPLY [9 votes]: What you get for your \$20 is a fixed list of half a billion primes of various sizes. If that's what you want, the price looks very reasonable -- it would take me months to generate a comparable list on my laptop. The only problem is that they don't say how they selected which primes to include in the list -- are they the first $n$ primes in the given range, or are they uniformly selected, or what? This makes them less reliable as input to a test suite, which is the most likely use for them.