Prime Number Explorer

Visualize the building blocks of arithmetic

Sieve of Eratosthenes

Watch the ancient algorithm discover primes by eliminating multiples.

Grid size (max 400)

Speed

Primes found0

Composites marked0

Current factor--

Pi(n)0

Prime Composite Current factor Being eliminated

Prime Factorization

Decompose any integer into its prime factors.

Enter a number

Enter a number and click Factorize.

Primality Test

Test whether a number is prime using trial division. Shows divisibility details.

Enter a number

Enter a number and click Test.

Twin Prime Finder

Twin primes are pairs (p, p+2) where both are prime. Find all twin primes up to a limit.

Search up to (max 100000)

Twin pairs found0

Largest pair--

Ulam Spiral

Arrange natural numbers in a spiral and highlight the primes. Discovered by Stanislaw Ulam in 1963, the surprising diagonal patterns remain unexplained.

Spiral size (odd, max 501)

Numbers0

Primes0

Density0%

Prime Counting Function π(n)

The prime counting function π(n) gives the number of primes less than or equal to n. Compare with the approximation n/ln(n) from the Prime Number Theorem.

Count up to (max 100000)

π(n) exact n / ln(n) Li(n) (log integral)