Line up the numbers 1 through 100, cross out every multiple of 2, then every multiple of 3, and keep going like that — and some numbers will still be standing at the end. Those numbers are the "primes." This method has a special name: it's called the "Sieve of Eratosthenes," after the ancient Greek mathematician who invented it.
A prime number is a number that's only divisible by 1 and itself — like 2, 3, 5, 7, 11. When kids first learn this, they often ask "why isn't 1 a prime?" By definition, a prime must have exactly 2 divisors (1 and itself), but 1 only has 1 divisor, so it's excluded from the primes. This point trips people up easily, so it's worth stopping to make sure it's clear.
What makes the Sieve of Eratosthenes so interesting is that you can discover the pattern with your own eyes. Color in the multiples of 2 on a 100-square grid and regular vertical columns appear; color in the multiples of 3 and a diagonal pattern shows up. Watching these visual patterns, kids naturally pick up an intuitive feel for the relationship between multiples and divisors.
Primes are more than just a math concept — they're deeply tied to the security technology we use in daily life. A lot of the encryption behind online banking and online shopping relies on the fact that it's extraordinarily hard to factor the product of two very large primes back into those original two primes. In other words, the concept of a prime number that elementary schoolers learn is also, in a very real sense, the core principle behind modern internet security.
Keep hunting for primes and one interesting question leads to another. Do primes go on forever? The answer is yes — over 2000 years ago, the Greek mathematician Euclid already proved there are infinitely many primes. There's also a pair called "twin primes," two primes exactly 2 apart, like 3 and 5, or 11 and 13 — and whether twin primes keep showing up no matter how large the numbers get is still an unsolved problem that mathematicians haven't been able to prove either way. Even today, mathematicians and computers around the world are collaborating on projects to find primes so enormous they have tens of millions of digits. Once kids realize that a simple activity like finding primes in a 100-square grid connects to a living mathematical problem that researchers worldwide are still working on right now, they may never look at primes the same way again.
As a hands-on activity, printing out a 100-square grid and crossing out multiples by hand works well, but it has the downside of taking longer and longer as the numbers get bigger, since there's more to cross out. Our activity page shows this process quickly as an animation, and also lets you click any number yourself to cross out its multiples all at once. You can see at a glance which number's multiples get crossed out first, and which numbers end up remaining as primes. After finding all the primes up to 100 together, having your child dig through the table themselves to answer questions like "which one's the biggest prime here?" or "where does the next prime after 97 show up?" builds an intuition that lasts far longer than simple memorization. Coloring in the whole table, counting up how many primes are left, and guessing how many primes there are up to 100 before checking the answer is also a wrap-up activity kids tend to enjoy.