Hunt every prime by elimination
Tap the smallest active number — its multiples chain-collapse to gray. Whatever stays alight is prime. Four levels escalate from 1–30 up to a 1–100 speedrun where the optimal play is exactly four taps: 2, 3, 5, 7.
The Sieve of Eratosthenes is the oldest known algorithm for finding every prime number up to N. This animated game lets you tap one prime at a time and watch its multiples fall together — so primality stops being a memorized list and becomes a chain reaction you can see.
Aligned with CCSS 4.OA.B.4 (factor pairs, prime/composite). Recommended for Grades 4–6.
Number theory · 4 mechanics
Each level changes the verb. Execute, predict, decide, recognize — the same prime-hunting algorithm trains four different ways of thinking.
Number theory explorer
Sieve of Eratosthenes is built for students who need factors, primes, composites, GCF, and LCM as visible structure. It gives the page a clear search purpose: learn the model, manipulate it, then continue into the matching grade-level practice.
Sieve of Eratosthenes helps when a student can copy a procedure but cannot explain why it works. The demo slows the idea down into a visible model before sending the learner to guided missions.
Learning goals
How to play
Continue with guided practice
A 2,200-year-old algorithm that finds every prime up to N. You start with 2, mark every multiple of 2 as composite, then move to the next unmarked number (3), repeat. Whatever survives is prime.
Every composite n must have a factor ≤ √n. So once you have swept every prime up to √N, no composites can remain hidden — every survivor is prime. From 1 to 100, that means stopping after 7.
Exactly four — 2, 3, 5, 7. Those primes sweep every composite in the range, and 11 > √100 = 10, so no further sweeps can change the outcome.
Grades 4–6, aligned with CCSS 4.OA.B.4 (factor pairs, prime/composite). Older students still benefit from the visual proof of the √N stopping rule.
