Urgent!!!! I have a Social Security Number!?

I was adopted back in 1963. I found my biological Mother 15 years ago but she would never tell me who my biological father is. Unfortunately, she past away last March and when I went through her paperwork, I found out she also gave birth to a baby girl 1 year later in 1964 which she never told me about either. I have her Fathers name and Social Security number. How can I find him? I have already contacted the SS office and they said they couldn't give me any information. I wish I knew someone that could look this SS number up and tell me where he lives or if he's even still alive.