What quantity did you change?
Labs / Mathematics
Sieve of Eratosthenes
Start with every whole number from 2 up. Circle the smallest survivor, cross out all of its multiples, and repeat — whatever is left standing is prime. Press Play to watch it run, or drag across the grid to sieve straight to a number.
Labs / Mathematics / Sieve of Eratosthenes
Sieve of Eratosthenes
Start with every whole number from 2 up. Circle the smallest survivor, cross out all of its multiples, and repeat — whatever is left standing is prime. Press Play to watch it run, or drag across the grid to sieve straight to a number.
Why it matters
Why explore this?
Mathematics helps us describe patterns precisely and predict what comes next. This model turns an abstract relationship into something you can change and observe.
Explore
Try the model
primes 0sieving —density 0.000
Investigate
Questions to test
Predict first, try it in the model, then use what you observe to answer.
What to try
- Once you have struck out the multiples of 2, 3, 5 and 7, why is everything still standing below 121 guaranteed to be prime?
- Turn on “colour by smallest factor.” Which colour claims the most squares, and why should that one always win?
- Push N up to 400 and watch the density readout. Do primes get rarer as the numbers grow, or does the thinning slow down?
- Every prime except 2 and 3 sits right next to a multiple of 6. Can you spot that pattern in the coloured grid?
- Can you find two primes that differ by just 2 — and do these twin pairs keep appearing no matter how far you sieve?
Explain
Make sense of what happened
State the pattern in words, test it with another example, and then connect it to the mathematical rule or representation shown in the model.
Check
Before you leave
What pattern did you observe?
Does the pattern work for another example?
If you can answer all three using evidence from the model, you understand the main idea. If not, return to Explore and change one setting at a time.