Conceptually, any information created or consumed outside your organization is not valid as part of a surrogate key, so SSNs are not a surrogate key. Furthermor

Conceptually, any information created or consumed outside your organization is not valid as part of a surrogate key, so SSNs are not a surrogate key. Furthermore, any time you reveal the primary key, that key can become the thing that people come to depend upon to find that database row, which leads to the possibility that someday, someone will have an important need for some primary keys to change, even if the primary key was supposed to be a surrogate key. The longer a database lives, the more likely that surrogate keys morph into natural keys. That's what happened to SSNs.