ts-x-prime
Version:
Library for working with prime numbers
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Markdown
# ts-x-prime
A lightweight TypeScript library for working with prime numbers: generate primes, test for primality, and use the AKS primality test.
## Installation
```bash
npm install ts-x-prime
```
or with pnpm:
```bash
pnpm add ts-x-prime
```
or with yarn:
```bash
yarn add ts-x-prime
```
## Features
| Function | Description |
| -------------------- | ---------------------------------------------------------------- |
| `generateSieve(n)` | Generates a boolean sieve of Eratosthenes up to `n` |
| `sieveToPrimes(s)` | Converts a sieve to a list of primes |
| `isPrimeSieve(n, s)` | Checks if `n` is prime using a precomputed sieve |
| `isPrime(n)` | Checks if `n` is prime using the 6k ± 1 optimization |
| `isPrimeAKS(n)` | Checks if `n` is prime using the AKS primality test (slow) |
| `zetaReal(s, terms)` | Approximates the Riemann zeta function for real `s` |
| `zetaEuler(s, max)` | Evaluates ζ(s) via the Euler product using primes up to `max` |
| `gamma(z)` | Computes the gamma function for a complex number `z` |
| `eta(s, terms)` | Dirichlet eta function η(s) for complex `s` with specified terms |
| `zeta(s, terms)` | Approximates ζ(s) for complex `s` using analytic continuation |
## Usage Examples
```ts
import {
generateSieve,
sieveToPrimes,
isPrimeSieve,
isPrime,
isPrimeAKS,
zetaReal,
zetaEuler,
gamma,
eta,
zeta,
Complex,
} from 'ts-x-prime'
// Generate primes using sieve
const sieve = generateSieve(100)
const primes = sieveToPrimes(sieve) // [2, 3, 5, 7, 11, ..., 97]
// Check using sieve
console.log(isPrimeSieve(37, sieve)) // true
console.log(isPrimeSieve(40, sieve)) // false
// Check using 6k ± 1 method
console.log(isPrime(29)) // true
console.log(isPrime(35)) // false
// Check using AKS (slow)
console.log(isPrimeAKS(13)) // true
console.log(isPrimeAKS(15)) // false
// Real zeta function
console.log(zetaReal(2)) // ~1.6449 (π²/6)
// Zeta via Euler product
console.log(zetaEuler(2)) // ~1.6449
// Gamma function
console.log(gamma(new Complex(0.5, 0))) // ~1.772 (√π)
// Dirichlet eta
console.log(eta(new Complex(1, 0), 10000)) // ~ln(2)
// Full zeta function (complex)
console.log(zeta(new Complex(2, 0))) // ~1.6449
```
## Notes
- `isPrimeAKS` uses the deterministic AKS algorithm and is intended for theoretical or educational use. It's very slow for large inputs.
- `isPrime` uses the 6k ± 1 method, which is efficient for medium-sized numbers.
- `zetaReal`, `zetaEuler`, `zeta`, `eta`, and `gamma` are provided for exploration of analytic number theory.
- For large batches of prime checks, prefer generating a sieve first.
## License
MIT © [rekmixa](https://github.com/rekmixa)