Some numbers are like bricks, and some are built from bricks. Prime numbers are the bricks, the ones that cannot be split into equal groups. Here is a two thousand year old trick for finding them, and a little game where you find them yourself.
#What you do
Write the numbers from 2 up to 100 in a grid. Start with 2. Keep 2, then cross out every number you reach when you count by twos: 4, 6, 8, and so on. Move to 3, keep it, and cross out 6, 9, 12, and the rest. Do the same for 5, then 7. When there is nothing left to cross, stop. The numbers still standing are the primes. You can try this with a pencil, or you can play it and watch the grid clear.
#What is really happening
Every number you cross out is a multiple, which means it is made by multiplying smaller numbers. Think of 12 as 3 groups of 4, or 2 groups of 6. It comes apart neatly, so it is not a prime. A number like 7 will not come apart. You cannot share 7 marbles into equal rows without one left over. That stubborn, cannot be divided quality is exactly what makes a number prime. This crossing out method has a name, the Sieve of Eratosthenes, after a Greek thinker who used it over two thousand years ago. A sieve is a kitchen strainer, and this one lets the ordinary numbers fall through and keeps the primes behind.
#Where it shows up
Primes are not just a puzzle. They are the building blocks of every other whole number, the way letters build words. When you send a message online, very large primes help keep it private and safe. So this old game with a pencil quietly powers a lot of the modern world.
#The short version
- Cross out the multiples of 2, then 3, then 5, and keep going.
- The numbers left standing cannot be divided evenly, so they are primes.
- This trick is called the Sieve of Eratosthenes, over two thousand years old.