One thing I enjoy doing when I’m bored is entering random numbers into a calculator and doing a prime factorization on the result. In September 2022, when doing this sort of goofing around, I tried doing a Knight’s Tour around the edge of the part of a calculator’s keypad that contained the numbers 1 through 9 and then find the prime factors of those numbers. For example, if I started at 7 and finished at 2, like this:
I’d end with the number 76,183,492 (this was as far as I could go as my calculator only held 8 digits)).
As I fooled around with the numbers generated this way, I discovered something interesting: all 16 numbers generated by doing a Knight’s Tour like this are divisible by both 11 and 101. Allow me to demonstrate:
Fun fact: the two numbers generated by this tour are the only two such numbers that have 11 as a prime factor twice.
Four other factors are shared amongst some of these numbers: