Write the numbers 2 to 100 in a grid. Circle 2, then cross out every other multiple of 2. Circle 3, cross out multiples of 3. Repeat with 5 and 7. Whatever survives is prime.
Quick check
When sieving the numbers up to 100, why is it enough to cross out multiples of just 2, 3, 5 and 7?
Your turn
Is 91 prime? Use the 'check primes up to √91' rule (√91 ≈ 9.5).
Eratosthenes invented this sieve around 240 BC. The exact same procedure still powers prime tables today.
Recap
- Write 2–100, circle 2, cross its other multiples; repeat with 3, 5, 7.
- Survivors are the primes — 25 of them below 100.
- You only sieve with primes ≤ √100 because every composite ≤ 100 has one.
- This is the Sieve of Eratosthenes.
Why only up to 7?
If a number under 100 isn't divisible by 2, 3, 5, or 7, it can't be divisible by anything else either — because the smallest factor of a non-prime is at most √n.
Eratosthenes invented this method around 240 BC. It still works exactly the same today.