Talking primes using Dirk Brockmann’s “Prime Time” explorable

I’ve been a huge fan of Dirk Brockmann’s explorable math activities since I first learned about them. The full list is here:

Dirk Brockmann’s Explorables

Today’s project was inspired by the “Prime Time” program – direct link here:

Dirk Brockmann’s Prime Time Explorable

I started the project today by asking my son to tell me some things he knew about primes. He gave the definition of a prime numbers, explained how we know that there are infinitely many primes, and talked about twin primes, though he apologized for not knowing how to prove that there were infinitely many twin primes:

Next I showed him the polynomial n^2 + n + 41 and we talked about this equation producing a lot of primes.

Now we went to the “prime time” explorable and my son talked about what he saw in the first two examples -> the Ulam spiral and the Sack spiral.

Finally we looked at the last two patterns -> the Klauber triangle and the Witch’s spiral.