I decided to try out the first problem with my younger son this afternoon and we ended up having a really nice discussion. The problem is:

Is 11 the largest prime number that has all the same digits?

There’s a lot of great math ideas hiding in the problem.

Here’s how we got started – I love hearing the progression of ideas that he has all the way to the end of the movie:

By the end of the last movie he came to the conclusion that if there was a prime number larger than 11 that had all of the same digits, the repeating digit would have to be 1. So, the next thing we did was explore the first couple of numbers made with repeating 1’s:

After realizing that even 11,111 was going to be a challenge to try to factor we end upstairs to play on Mathematica. We made some pretty quick progress! Also, seeing the non-prime results on Mathematica also helped him see some patters in the non-primes that he hadn’t notices before – score one for some computer math!

Finally, I showed him the starting list on the Integer Sequence Database that shows the first few primes of the type we were looking at:

This was a really fun project – thanks to Matt Enlow for sharing this great list of problems!