Number theory lab

Prime Explorer

Watch the sieve of Eratosthenes discover every prime up to your limit. Click any integer for a factor breakdown; play, pause, or step through each mark.

Educational walkthrough
SlowFast

Ready. The sieve will walk integers from 2 upward, keep primes, and strike their multiples.

Integers 1–50

Tap a cell for details

PrimeCompositeMarking nowPending

Number details

Click any integer in the grid to inspect it. Composites show a full factor breakdown; primes explain why they have no proper factors other than 1 and themselves.

  • Prime — only divisors are 1 and itself
  • Composite — product of smaller primes
  • Being marked — multiple of the current prime

Primes found

0 / π(50) …

New primes appear as the sieve selects each unmarked integer.

No primes yet — press Play to begin.

How the sieve works

  1. List integers from 2 to N (1 is set aside).
  2. The first unmarked number is prime — call it p.
  3. Strike every multiple of p (from p² onward) as composite.
  4. Repeat with the next unmarked number until p² exceeds N.
  5. Everything still unmarked is prime.