Post is kind of unclear -
do you need permissable purpose to search for someone by their social security number
Reading your post as written I would imagine the purpose would be to find the person and it seems as though it would indeed be permissible, however, not particularly practical.
I would think that you would get better results asking 'Have you seen Bob?' than asking 'Have you seen 123-45-6789?'.
Maybe your post refers to searching particular records for information regarding a person?
A little more detail would probably allow someone to give you a good answer here.
Hope you get a good answer -
wtd