Is 97 prime? Is 221? One of them divides by 13, and finding which by hand is exactly the kind of homework filler a machine should do. This tool tests any number up to 15 digits and tells you why, and also lists every prime up to 50,000.
Updated September 03, 2026, after a fresh review, with updated visuals and links.
Two modes: check and generate
Check mode answers instantly and educates: not-prime answers come with the smallest factor found (221 = 13 x 17), prime answers come with the definition that makes them special.
Generate mode runs the sieve of Eratosthenes: cross out multiples of 2, then 3, then 5, and what survives is prime. Up to 50.000 it returns in milliseconds, showing the count first.
Patterns worth noticing on the list: primes thin out as numbers grow, all primes above 3 sit next to a multiple of 6, and 2 is the only even prime ever.
Worth remembering
- For testing big candidates, remember you only need to check divisors up to the square root: proving 9,999,983 prime takes 1,581 tries, not ten million.
- Twin primes (like 29 and 31) are pairs two apart; hunting them in the generated list is a genuinely fun numbers game.
Frequently asked
Is 1 a prime number?
No. Primes have exactly two positive divisors; 1 only has one. This convention keeps the fundamental theorem of arithmetic (unique prime factorization) true.
Why do primes matter outside school?
Modern encryption (RSA) depends on multiplying two huge primes being easy while splitting the result back into them is brutally hard. Every secure login rides on that asymmetry.
