Prime number checker & generator

How it works

Primality is tested by trial division: after handling 2 and 3 as special cases, the checker only tries odd divisors up to the square root of the number, since any factor larger than the square root would have a matching factor smaller than one already tested. The "primes up to" list runs that same check against every integer up to your limit.

FAQ

Why is the "primes up to" limit capped at 1,000,000 and the list capped at 2,000 primes?

Trial division doesn't scale — checking every integer up to a million with hand-rolled division in the browser would freeze the tab, so the input is capped and the displayed list stops at the first 2,000 matches to stay responsive.

Is 1 considered a prime number here?

No — by definition a prime has exactly two divisors, 1 and itself, and 1 only has one, so the checker correctly marks 0, 1, and any negative number as not prime.