# prime-number

is a recursive function to check if a number is prime (and a benchmark to test how slow it is :)

Is it 1 a prime? Some years ago I composed a djembe rhythm based on prime numbers, and it sounds better if 1 is considered prime. Casually, the algorithm implemented here defines 1 as a not prime.

## Usage

As you might expect, you can do

``````const isPrime = require('prime-number')

console.log(isPrime(19)) // true
``````

There is a list of few primes available, if you want to use it

``````const primeNumberList = require('prime-number/list')
``````

You can benchmark other primality check algorithms.

``````const isPrime = require('yet-another-primality-check')
const benchmark = require('prime-number/benchmark')
const from = 1000
const to = Number.MAX_SAFE_INTEGER

benchmark(isPrime)(from, to)
``````

Using a oneliner, let’s check few primality check packages found on npm.

``````# node -e "require('prime-number/benchmark')(require('prime-number'))(10000, 100000)"
Found 8363 primes
Primality benchmark: 44.703s

# node -e "require('prime-number/benchmark')(require('is-prime'))(10000, 100000)"
Found 8363 primes
Primality benchmark: 14.885ms

# node -e "require('prime-number/benchmark')(require('check-prime'))(10000, 100000)"
Found 8363 primes
primality benchmark: 61.613ms
``````

So I can state that

My algorithm sucks! 🐸

## Installation

With npm do

``````npm install prime-number
``````

Or copy and paste the code below.

## Source

First of all, do not check if num is an integer or positive or less than `Number.MAX_SAFE_INTEGER`. You can do it with some other function before calling `primeNumber`.

``````// Remember if a number is prime.
const memoize = { isPrime: {}, isNotPrime: {} }
memoize.isNotPrime[1] = true
memoize.isPrime[2] = true

/**
* Check if a number is prime.
*
* @param {Number}
*
* @returns {Boolean}
*/

// Avoid computing twice.
if (memoize.isPrime[num]) return true
if (memoize.isNotPrime[num]) return false

const knowPrimes = Object.keys(memoize.isPrime)

for (let i = 0; i < knowPrimes.length; i++) {
const p = Number(knowPrimes[i])

if (num === p) return true

if (num % p === 0) {
memoize.isNotPrime[num] = true
return false
}
}

for (
let i = 3;
// Do not excede the square root of num.
i * i <= num;
// All prime numbers are 1 or 5 modulo 6.
// Since we start with 3, this will do: 3 -> 5 -> 7 -> 11 ... +2 -> +4 -> +2 -> +4 ...
i = i % 6 === 1 ? i + 4 : i + 2
) {
if (primeNumber(i)) { // <-- Recursion here!
if (num % i === 0) {
memoize.isNotPrime[num] = true
return false
}
}
}

memoize.isPrime[num] = true
return true
}
``````

Export `primeNumber` function

``````module.exports = primeNumber
``````