Prime Sieve
Animate the Sieve of Eratosthenes on the 100 chart. A volunteer narrates as each prime lights up and its multiples get crossed out one by one.
The sieve
Start with every number from 2 to 100. Walk through them in order:
- Find the first unmarked number — it’s prime. Light it up.
- Cross out all of its multiples — they can’t be prime, because they’re divisible by something.
- Repeat until you’ve checked everything up to 100.
Whatever’s left unmarked at the end is a prime number.
Why does it work?
A composite number (non-prime) must have at least one factor smaller than itself. That smaller factor will be found first, and will cross out the composite number during its sweep. So every composite number gets eliminated before we ever reach it.
Things to watch for
2’s sweep wipes out nearly half the chart in one pass — every even number above 2.
After 7, no new crossings — because the next prime is 11, and 11² = 121 > 100. Every composite under 100 has a factor ≤ 10, so they’re already gone.
25 primes live below 100. There’s no obvious pattern to predict which numbers they are — that’s part of what makes primes endlessly interesting.
Who invented this?
Eratosthenes of Cyrene, a Greek mathematician, around 240 BC. He also calculated the circumference of the Earth — and got within 2% of the right answer — using shadows and geometry.