// Number
Prime Number Generator online
List all prime numbers up to any limit - Sieve of Eratosthenes
by
CHUNKY
MUNSTER
MUNSTER
Prime Number Generator implements the textbook Sieve of Eratosthenes: it allocates a boolean array of length N + 1, repeatedly walks through unmarked integers starting at 2, and crosses out every multiple. Whatever survives are the primes up to N. Time complexity is O(n log log n), which is the fastest known sieve for this problem class.
The 100,000 cap keeps the in-memory bit array small enough for mobile browsers; for larger ranges a segmented sieve and a desktop language are the right tools. This math tool provides a fast way to generate an integer sequence of primes for research or development. The output panel shows the prime counting result and the largest prime in the range, both useful for quick checks. The full list can be downloaded as plain text for use in other programs.
Write down every integer from 2 to N. Take the first uncrossed number (2), mark every multiple of it as composite, then move to the next uncrossed number and repeat. What remains uncrossed at the end are exactly the primes.
The sieve allocates one boolean per integer in the range, so memory grows linearly with the limit. 100,000 keeps the page responsive on phones and laptops; higher limits are better suited to a segmented sieve in a desktop language.
Asymptotically about N / ln(N) - the prime number theorem. Up to 1,000 there are 168 primes; up to 10,000 there are 1,229; up to 100,000 there are 9,592. The exact count for your chosen limit is shown in the stats row.
Yes, in ascending order. The sieve naturally produces primes in increasing order because it walks the integers from 2 upward.
Explore the full suite of Number tools and 290+ other free utilities at Chunky Munster. For rapid integer sequence exploration, bookmark this Prime Number Generator.