Generate Prime Numbers

An ancient algorithm that finds all primes up to n by iteratively marking multiples of each prime starting from 2. Every number that remains unmarked at the end is prime. For large n, sieving is much faster than trial-dividing every candidate.

10,000,000. At that size the sieve allocates about 10 MB (one byte per index) and runs in 1-2 seconds on a modern laptop. Pushing higher risks allocation failures on low-memory devices.

Very fast. Up to 100,000 it completes in a few milliseconds; up to 1,000,000 in ~30 ms; up to 10,000,000 in 1-2 seconds. The loading state only kicks in for 500k+ to give the UI a chance to repaint.

Yes – comma, newline, or space. Switching the separator re-renders from the cached prime array instantly, so you can toggle freely without re-sieving.

Exactly 78,498 – the famous value for π(10^6). Enter 1,000,000 as the limit and the stats line will confirm the count.

The largest difference between two consecutive primes in your range. For primes up to 100 the largest gap is 8 (between 89 and 97). It’s a quick way to spot prime deserts without scanning the full list.

π(n)/n – the fraction of integers up to n that are prime. It drops roughly like 1/ln(n) by the Prime Number Theorem, so density falls from 25% at n=100 to about 7.85% at n=10^6.

Cryptography (RSA/DH key selection), number-theory experiments, primality-test benchmarks, hash-table sizing, coding interview problems, and teaching material for algorithm classes.

Yes and yes. The sieve runs 100% client-side – no server call, no analytics on your input, no data retention – and the tool is free with no sign-up or usage caps.

Yes. After the page has loaded, every sieve runs locally in your browser. Disconnect from the internet and the tool keeps generating primes.