Watch the classic prime-finding algorithm strike out composite numbers one factor at a time. Pick a range, press Run, and see primes emerge from the grid. Twin primes are highlighted in blue.
The Sieve of Eratosthenes (c. 240 BCE) finds all primes up to n by repeatedly taking the next unmarked number as prime and marking all its multiples (starting from p²) as composite. Its time complexity is O(n log log n) — among the fastest classical ways to generate primes in a range. Twin primes are pairs (p, p+2) that are both prime; the twin prime conjecture (whether infinitely many exist) remains famously unresolved.