Random Token Generator - Not Really Random

We have the need to have a random token (a 16 char alphanumeric field) to be used as the key for one of our SQL tables. I have created a random token generator, however after only 3 months in production, it appears that we had an instance where a token that already existed in the tables was created. There are 3810 records currently in the database so it isn't like there are billions of records there.

I contacted an old college buddy of mine who is a mathematician, and he claims, assuming that random really does mean random, that the chances of getting a duplicate token are 1 in 79.5 septillion (79,500,000,000,000,000,000,000,000).

So my conclusion is that this was either a complete freak of nature occurance, or my random generator isn't really all that random. Here is the code behind how I am generating this: Code: