# The primes such that removing digits from the right end leaves another prime

The number 73,939,133 is prime. Keep removing a digit from the right end. Each of the remaining numbers is prime.

How to find other numbers with this property?

I don't think there's any particularly elegant way to solve this. So I wrote an algorithm which started with the primes $1$ through $9$ and, at each step, it took the previous list, and made a new list out of the previous list, with elements for each of the digits $0$ through $9$ (though, really only $1$, $3$, $7$ and $9$ need to be checked since even digits and $5$ never end a prime in decimal), and checked this new list for primality. When the list was empty, I stopped iterating, since this meant that there were no primes of a certain length that satisfied the property, which means that no higher length prime could exist, certainly. I got the following list: