Sieve of Eratosthenes (TypeScript)

A readable, zero-dependency implementation of the Sieve of Eratosthenes in TypeScript.
Generate all prime numbers up to a given limit with classic algorithmic efficiency.

Installation

npm install sieve-of-eratosthenes-ts

Usage

Import the function and call it with any positive integer limit:

import { sieveOfEratosthenes } from 'sieve-of-eratosthenes-ts';

console.log(sieveOfEratosthenes(100));
// [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97]

If the full name feels too verbose, use a local import alias:

import { sieveOfEratosthenes as sieve } from 'sieve-of-eratosthenes-ts';
console.log(sieve(100));

The package exports only one function, so you stay in full control over naming.

Algorithm

The Sieve of Eratosthenes marks multiples of each prime starting from 2, leaving only primes behind.
It runs in O(n log log n) time and uses O(n) space.

| Metric | Value | | :--- | :--- | | Time complexity | O(n log log n) | | Space complexity | O(n) | | Limit support | Up to ~10⁷–10⁸ in Node (memory‑bound) |

For larger limits, a segmented sieve is recommended.

Testing

npm test

Tests cover edge cases (limit < 2) and verify correct prime sets up to 100.

Contributing

Pull requests are welcome. For major changes, please open an issue first to discuss what you would like to change.

License

MIT © 2026 0xA672

See Also

For a high‑performance Rust equivalent, check out primal – a state‑of‑the‑art prime sieve with estimation and factorisation, maintained by Huon Wilson, former Rust core team member.