My family’s phone number when I was a child was both a palindrome and a prime: 7984897.

My parents had had the number for two decades without noticing it was a palindrome. I still remember my father’s delight when he got off a phone call with a friend: “Doug just said, ‘Hey, I dialed your number backwards and it was still you who answered.’ I never noticed that before!”

A few years later, around 1973, one of the other math nerds at my high school liked to factor seven-digit phone numbers by hand just for fun. I was then taking a programming class—Fortran IV, punch cards—and one of my self-initiated projects was to write a prime factoring program. I got the program to work, and, inspired by my friend, I started factoring various phone numbers. Imagine my own delight when I learned that my home phone number was not only a palindrome but also prime.

Postscript: The reason we hadn’t noticed that 7984897 was a palindrome was because, until around 1970, phone numbers in our area were written and spoken with the telephone exchange name [1]. When I was small, I learned our phone number as “SYcamore 8 4 8 9 7” or “S Y 8 4 8 9 7.” We thought of the first two digits as letters, not as numbers.

Second postscript: I lost contact with that prime-factoring friend after high school. I see now that she went on to earn a Ph.D. in mathematics, specialized in number theory, and had an Erdős number of 1. In 1985, she published a paper titled “How Often Is the Number of Divisors of n a Divisor of n?” [2]. She died two years ago, at the age of sixty-six [3].

[1] https://en.wikipedia.org/wiki/Telephone_exchange_names

[2] https://www.sciencedirect.com/science/article/pii/0022314X85...

[3] https://www.legacy.com/us/obituaries/legacyremembers/claudia...