I'm not sure if this is a legitimate business but ...

I'm not sure if this is a legitimate business but someone contacted me yesterday about a job. She was adamant about providing her with my personal information (my date of birth and my social security number). I advised I wasn't comfortable with giving that information over the phone & told her I would respond to her emails (she sent 2 before the phone call). I never responded because I don't think this business is in fact real. This morning I received 7 phone calls from her in an hour (I blocked the number but it still shows when a call is rejected) & another email. At this point I just want the calls to stop, whether this business is real or not, 7 calls in an hour can be considered harassment.