Odd facts primes pick up in a sieve
Multiples of small primes eat the board first, so the grid looks noisy early, then suddenly quiet near the end.
2 is the only even prime, so the first sweep removes half the board in spirit before you even feel the rhythm of larger steps.
When you raise N, the count of primes near N grows roughly like N divided by the natural log of N, which is why a run to 1000 feels generous while a run to 200 still teaches the pattern.
Three jobs this fits
| Situation | What you do here | What you walk away with |
|---|---|---|
| Lecture prep | Set N to 60, run slow, point at the first few waves | A shared visual for why composites collapse in families |
| Homework check | Match your upper bound, use instant, copy the list | A comma-separated sequence you paste into a proof or table |
| Competition warm-up | Toggle fast mode with N near 240 | Quick recall of density without hand arithmetic |
Paper, Python, or this tab
Hand sketches reward muscle memory. A short script rewards scale. This page rewards immediacy: you see the strike pattern without installing a kernel.
When you need symbolic crunching elsewhere on the site, the Scientific Calculator stays handy for follow-up arithmetic, while the Mathematical Constants Generator pairs well if you jump from primes into constants for estimates.
Reviewed March 2026. Processing stays in your browser tab; we do not store your N or your prime list.
Why stop at the square root?
Every composite n carries a factor pair. One factor is always at or below the square root of n, so once you have crossed multiples for every prime up to that root, no composite above survives.
The tool mirrors the classic loop: walk p from 2 upward while p squared still fits inside N. Each time p stays unmarked, you promote p, then strike p squared, p squared plus p, and so on.
The ceiling nobody likes talking about
We cap N at 1000 so phones stay smooth. Pushing higher belongs to segmented sieves or native code, not a tight DOM grid.
Animated mode uses timers, so switching tabs mid-run may feel jumpy. Instant mode avoids the choreography entirely.
Colour on a grid is not a theorem
The animation is pedagogy, not certification. Courses still ask for arguments about divisibility, not screenshots of a web board.
Use the output as a checksum after you reason by hand, or as a lecture prop while you narrate the logic aloud.
- Students: pair each run with a written trace of one prime pass, naming the first multiple you strike and why smaller multiples were already gone.
- Instructors: slow mode makes the “first survivor after a sweep” moment obvious without chalk dust.
- Self-study: copy a short list, then try to predict how many primes land between two squares before you rerun.
Density heuristics matter for intuition. The Mathematical Function Grapher helps when you pivot from counting primes to comparing smooth curves, because the sieve itself never draws π(x) against x.
Segmented sieves, wheels, and Atkin variants exist because memory and constant factors bite long before you exhaust mathematics. This page chooses a transparent trade-off: small N, obvious cells, zero server round trip.
If you export the list into another tool, keep the comma format or switch to newlines in your editor. The copy buffer is plain text on purpose so note-taking apps do not inject hidden markup.
