A simple iterator that generates all the prime numbers

primes.py

"""
primes provide a very simple iterator that's able
to generate all the prime numbers!

This is for teaching purposes only.
"""


class Primes:
    """
    Primes is an iterator that generates all the prime numbers.

    Its usage is simple:

    >>> for prime in Primes():
    ...     print(prime)
    2
    3
    5
    7
    11
    13
    

    This is for teaching purposes only and implements the most
    basic algorithm for primality testing. If you need to use
    this in a more formal setting, please revisit this code.
    For starters, I'd suggest using AKS primality testing.
    """

    def __init__(self, start=1):
        """
        init accepts a start values from where the iterator will begin.
        It does not need to be a prime number itself.
        """
        self.current = start

    def __iter__(self):
        return self

    @staticmethod
    def is_prime(n):
        """
        is_prime does a trial-and-error primality check.

        It basically loops through all the numbers from 0 up to n-1 checking
        for divisors.
        """

        # Note: we could loop up until sqrt(n).
        for i in range(2, n):
            # If n is divisible by any number other than
            # 1 and itself, its not a prime
            if n % i == 0:
                return False
        return True

    def __next__(self):
        """
        computes the next prime number by trial and error
        """
        # The first candidate is the next number in line
        next_prime = self.current + 1

        # While it is NOT a prime...
        while not self.is_prime(next_prime):
            # We try the next number
            next_prime += 1

        self.current = next_prime
        return self.current