Quote from: MTPcgr on January 08, 2014, 08:34:35 PM

Let's assume that I use this program to generate a vanity URL using the pattern 1Bill. What's to stop someone else from using the same program using the pattern 1Bill and ending up with the same private key that I got? How do I know that the private key the application generated for me is unique, safe, and not also going to be generated for someone else using the same pattern?

In theory, the odds of someone else being able to generate the same public key are incredibly low -- virtually impossible. The difficulty of doing that is the basis of the security of bitcoin.

However, flaws in the address generation software can reduce that difficulty, and there have been flaws.