ID

So I was thinking today about domain names and whatnot and had the thought, "why doesn't everyone have a domain name and telephone number that is the same as their social security number?" Then I thought, "why does a social security number have the same number of digits as a phone number?" (It doesn't, yeah, yeah, yeah.) So my social security number is available. Should I register a domain with it? If someone else does, can they exert copyright over my social security number?