I really enjoyed this site as most all of us math majors did! I am also in your 405 class and I really found it interesting about the number 73939133 and how it's the largest known prime that is right-trunctable. It really interests me to see what the next largest prime number will be and when we will find a largest prime that is also right trunctable like the one above. One interesting claim and proof I found on that site was this:

"Prove that every 9-digit prime (no leading zero) that has distinct digits

contains the digit 6 (I have a proof)"

Solution

Jim R. Howell sent (14/06/99) the following explanation:

"Consider any 9-digit number with distinct digits. If this number does not contain the digit "6", then it is the other 9 digits (0,1,2,3,4,5,7,8,9) in some order. But the sum of these digits is 39, so this 9-digit number is divisible by 3. Therefore, if "6" is missing, the number cannot be prime. A similar argument can be used to show that these 9-digit primes also contain the digits 0, 3, and 9."

I find it amazing how people look into this type of thing, if I was smarter or had more time I would definitely find myself having a lot of fun trying to discover things like this and all the other fun prime facts we've been learning about. That came off pretty nerdy but whatever haha…