ts-x-prime

A lightweight TypeScript library for working with prime numbers: generate primes, test for primality, and use the AKS primality test.

Installation

npm install ts-x-prime

or with pnpm:

pnpm add ts-x-prime

or with yarn:

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 | | new Goldbach(n).getPairs() | Getting goldbach pairs for n | | new Goldbach(n).getPrimes() | Getting goldbach primes for n |

Usage Examples

import {
  generateSieve,
  sieveToPrimes,
  isPrimeSieve,
  isPrime,
  isPrimeAKS,
  zetaReal,
  zetaEuler,
  gamma,
  eta,
  zeta,
  Complex,
  Goldbach,
} 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

// Getting goldbach pairs for 10
console.log(new Goldbach(10).getPairs()) // [[3, 7], [5, 5]]

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