Primeget (WIP)

Generates prime numbers algorithmically

Primeget is a prime number generator combined with a prime checking method to discard non-primes. It is capable of generating primes from a given range.

Generating the primes in n = 9_000_000_000_000_000 to z = 9_000_000_000_001_000 takes approximately ~29s.

A range between n and n + 1000 seems to be the sweet spot without crashing V8.

Usage

import primeget from 'primeget'

let primes = primeget(0, 10) // [ 2,  3,  5, 7, 11, 13, 17 ]

// Interesting things happen here. Anything above `n = 97` returns nothing, but `n <= 97` is notable.
primes = primeget(97, 0)
/*
[ 97 ]
*/

primes = primeget(10, 0)
let set = [...new Set(primes)].sort((a, b) => a - b)
/*
[
    3,   5,   7,  11,  13,  17,  19,  23,  29,  31,  37,  41,
   43,  47,  53,  59,  61,  67,  71,  73,  79,  83,  89,  97,
  101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157,
  163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227,
  229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283,
  293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367,
  373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439,
  443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509,
  521, 523, 541, 547,
  ... 229 more items
]
*/

Example

import Primeget from 'primeget'

let n = 9_006_999_999_998_000
let z = 9_006_999_999_999_000

console.time('Time')
let primes = primeget(n, z)
console.timeEnd('Time') // About 10 seconds

// remove duplicates and sort
primes = [...new Set(primes)].sort((a, b) => a - b)

console.log(primes)
console.log('Last:', primes.slice(-1)[0])
console.log('Total:', primes.length)

API

My goal was to create a simple API for this sheep counting prime number generator. It should be quite flexible. The CLI I built is an example of how it can be extended. Submit an issue if it doesn't meet your needs.

API Usage

import Primeget from '../api.js'
import { check } from '../primeget.js'

let primeget = new Primeget()

let isPrime = check(101) // true

check(n)

Check if n is prime

Returns true if prime, false if not prime

primeget.make(n, z)

Generate a set of prime numbers starting wih n until z.

This is an O(n) function and may crash things if the range is too great. I am not a mathematician, so O(n) may be wrong; please correct me!

primeget.get()

Return a sorted and filtered array of primes generated by primeget.make(n, z)

primeget.raw()

Return the raw numbers calculated by Primeget before sorting and filtering

primeget.length

Return the length of the sorted and filtered array of primes generated by primeget.make(n, z)

CLI

A simple CLi with some basic features.

CLI install

npm i primeget -g

CLI Usage

> primeget // initiates Primeget cli

// generate some primes
primeget > make 0 100

// print the array of primes
primeget > get

// print the length of array of primes
primeget > get -l

// print prime at the provided index
primeget > get 187

// print a random element from the array of primes
primeget > get -r

// print array of primes between 30 and 40
primeget > get 30 40

// print array of primes between 30 and 40
// along with length of the array of primes between 30 and 40
primeget > get 30 40 -l

// another way to print the length of the current set of primes
primeget > length

// print if a number is prime (not depedant on the Primeget generated primess)
primeget > check 111 // false

// quit Primeget
primeget > 'quit' or 'exit' or 'bye' or 'close' or 'end' or 'ctrl+c'

About

I'm not a mathemetician. But I can count sheep.

Nearly 20 years ago, I had a bout of insomnia. Instead of counting sheep that night, I calculated prime numbers starting with 0 + 1 != prime, then 1 + 1 = prime, then 1 + 2 = prime, and so-on, along with some subtraction between the previous two primes. I realized the system I devised worked with larger numbers, too.

I didn't know how to program very well at the time, so my attempt to test the pseudocode I wrote down was a failure. For the record, I slept very little that night.

I have since lost that pseudocode and forgot the details, but suddenly recalled parts of the methodology. Using pieces of that recollection plus a prime check and passing in previous primes, I have been successful at generating primes with this code.

Contribution

If you are a mathematician, it would be great to have your feedback and/or PR on this algorithm!

License

MIT