Prime generator via unbounded Sieve of Erathosthenes

unbounded-erathosthenes.py

#! /usr/bin/env python3

""" See this URL for an explanation of what we're doing here:
https://wthwdik.wordpress.com/2007/08/30/an-unbounded-sieve-of-eratosthenes/
"""

import itertools
import types

class Prime(types.SimpleNamespace):

    def __new__(cls, n, multiple):
        return super().__new__(cls, n=n, multiple=multiple)

    def update_multiple(self, value):
        """ Increase 'multiple' in steps of 'n' until it is >= value. """
        while self.multiple < value:
            self.multiple += self.n

def get_primes():
    """ Prime generator via unbounded Sieve of Erathosthenes. """

    yield 2
    prime_numbers = [Prime(n=2, multiple=2)]
    for candidate in itertools.count(3, step=2):
        for prime in prime_numbers:
            prime.update_multiple(candidate)
            if candidate == prime.multiple:
                break
        else:
            yield candidate
            prime_numbers.append(Prime(n=candidate, multiple=candidate))

if __name__ == "__main__":

    n = 9 # find the tenth prime number
    it = itertools.islice(get_primes(), n, n + 1)
    print(next(it))