Generators/iterators, Pythonicity, and primes

[John Posner]

Inspired by recent threads (and recalling my first message to Python
edu-sig), I did some Internet searching on producing prime numbers using
Python generators. Most algorithms I found don't go for the infinite,
contenting themselves with "list all the primes below a given number".

Here's a very Pythonic (IMHO) implementation that keeps going and going and
going ...:

from itertools import count
from math import sqrt

def prime_gen():
    """
    Generate all prime numbers
    """
    primes = []
    for n in count(2):
        if all(n%p for p in primes if p < sqrt(n)):
            primes.append(n)
            yield n

The use of all() is particularly nifty (see
http://code.activestate.com/recipes/576640/). And so is the way in which the
list comprehension easily incorporates the sqrt(n) optimization.

Question: Is there a way to implement this algorithm using generator
expressions only -- no "yield" statements allowed?

BTW -- thank you, John Machin, for the spanking ('I'd worry about "correct"
before "Pythonic"') in a previous message. I *did* manage to post a
correction to the needless conversion of a string to a list:

   b in list("\r\n\t")

... a few hours before your message arrived (Wed Apr 1 19:44:01 CEST 2009)!





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