We’ve now down a couple of projects on the latest Numberphile video on the Goldbach Conjecture:
Following those projects I thought it would be neat to let the computer run and find the numbers that could be written as a sum of two primes in many different ways (specifically, in more ways than any number less than it). Looking at those results produced a nice surprise:
A double surprise was that Numberphile had just (the day before) published a follow up Goldbach Conjecture video that talks a little bit about the idea that explains the pattern I was seeing:
Last night I walked the kids through some of the ideas. We first watched the end of the Numberphile video and then talked about it briefly.
Also, I was pretty under the weather yesterday, so sorry for the low energy from me in this project:
Next we moved on to looking at the Goldbach Comet and told them about the project I was looking at while they were up in New Hampshire hiking.
They noticed the same pattern that I saw and I showed them the prime factorizations of a few of the numbers on my list.
After we talked about the factoring, I wanted to show them another surprise – the Goldbach Comet looks surprisingly symmetric around the numbers that can be written as the sum of two primes in lots of ways.
Fianlly, we wrapped up the project by looking at the symmetry I mentioned above a bit more carefully. I’d like to explore this symmetry a bit more myself!
We’ve really had a fun set of projects on the Goldbach Conjecture. It is definitely accessible to kids and a great way to show them an unsolved problem in math!