Why do prime numbers make these spirals? | Dirichlet’s theorem and pi approximations

Prime numbers make these spirals because they follow special rules, just like how your toys line up when you arrange them by size or color.

Imagine you're drawing on a spiral notebook, every time you reach the end of a row, you move to the next one. If you color in all the prime numbers (those are numbers that can only be divided by 1 and themselves, like 2, 3, 5, 7), they start forming pretty patterns or spirals.

Now think about how your favorite candy comes in bags, sometimes it’s grouped by 2s, 3s, or other numbers. Dirichlet's theorem is like a rule that says: If you group candies (or numbers) by certain rules, there will always be an endless supply of prime candies in each group. It’s like saying no matter how you sort your toys, some special ones, the primes, will always show up again and again.

Pi comes into play because it helps us understand these patterns better. It's kind of like a helper that connects circles to numbers, making it easier to see why those spirals happen when we color in prime numbers on a spiral grid.