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Lesson 6 · Prime Numbers

The Atoms of Math

Some numbers refuse to be split. They're the building blocks every other number is made from. Let's hunt them.
Scene 1

What's a prime number? 🧱

A prime number is a number that only has two friends who divide it evenly: 1 and itself. Nothing else.

Take 7. Try to split it into equal groups: 2 groups? Doesn't work. 3 groups? Doesn't work. 4, 5, 6 groups? None work. Only 1 group of 7, or 7 groups of 1. 7 is prime.

But 6? Easy: 2 groups of 3, or 3 groups of 2. Not prime. A 2,300-year-old Greek named Eratosthenes found a clever way to catch all the primes at once. It's called a sieve — like sifting flour to keep only the good bits.

Scene 2 · The Sieve

Watch the primes appear ✨

Ready? The grid shows numbers 1 to 100. Tap "Next step" to start the sieve.
Scene 3 · Try it

Every number is built from primes 🧩

Here's the magical part. Pick any non-prime number. You can always break it into primes multiplied together. Try it:

60 = 2×2×3×5
Try 100, 24, 84, 365, your age, today's date…
The Big Idea

Primes are the atoms of math 🌟

2 · 3 · 5 · 7 · 11 · 13 · 17 · 19 · …

Every other number in the universe is built by multiplying primes together. They're like LEGO bricks — you can build any number from them. And they go on forever — there's no biggest prime.

Primes also keep your messages secret. When you send a text or visit a website, primes hundreds of digits long protect what you say. Math doing real work in the world, every second.