In the past, SSN were assigned sequentially within each SS office. Depending upon your age, your may be in the age group when SSNs started to be applied for at birth, and assigned immediately. That was done to enable parents to enter SSNs on their income taxes to claim dependents. So, it is not surprising at all that the person with an adjacent SSN was from the same area and about the same age. It used to be possible to look at the first 5 digits and know what part of the country the person lived in when they applied, sometimes even down to the SS office they visited. There was an assignment scheme similar to that used for US and Interstate highway numbers (odd numbered Interstates run north/south from I5 in California east to I95 along the East Coast. I97 and I99 were afterthoughts).
The problem you identified regarding identity theft is a real one, and SSN are no longer assigned in the way I described for just that reason. I am youth-challenged, and in my cohort, it was common for SSN to be applied for when you started work, although it could be done earlier. I can remember going to the SSN office to apply. My father took me and my brother. I was about 8 years old. My brother and I were assigned sequential numbers.
Shopping Southeast Pennsylvania, Delaware above the canal, and South Jersey since 2008