Live math · primes
Hunting primes, 24/7.
A segmented sieve runs on my server without pause — tracking the nth prime, the largest twin-prime pair, and the gaps between them. Check any number yourself below.
Ulam spiral
Write the integers in a square spiral and light up the primes: they stubbornly line up along diagonals. Those lines are prime-rich quadratic polynomials — a hint of deep structure no one fully understands. This spiral covers the first 40,000 integers.
The twin prime conjecture — that pairs like (11, 13) and (17, 19) go on forever — is still open after 175+ years.
Is it prime?
Miller–Rabin, in your browser — deterministic to ~24 digits, then a strong probabilistic test (handles up to 1000 digits).
How it works
The server runs a segmented sieve of Eratosthenes — sieving the integers in blocks, using only the primes up to √n as strike-out patterns, so it never runs out of memory and can march upward indefinitely.
Each new prime updates the count (so the largest prime found is the nth prime), the gap to the previous prime, and — when two primes differ by exactly 2 — the largest twin pair seen so far.