Is she interested if she doesn’t give her social or number?

So I met this girl at the gym and seen her a few times and I talked to her, asking if I was interrupting anything she said oh don’t worry and giggled blushing a bit. I asked for her name and talked for a bit then she asked for my name before I left. A week or so goes by and I see her again and she remembered my name and everything then we started to talk again she was giggling and blushing a bit, smiling and asking me questions. She was stuttering a bit when we’re talking. Before I left I asked if she wanted to workout together or talk outside of the gym (like asking for social or number) she said that she prefers working out alone but if I see her again while working to talk to her. Is she interested?
Is she interested if she doesn’t give her social or number?
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