Generators/iterators, Pythonicity, and primes

[Mark Tolonen]

"John Posner" <jjposner at snet.net> wrote in message 
news:AF9FBCC3A7624599A6F51BAD2397EA46 at AMDUP...
> 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

p <= sqrt(n) works a little better :^)

-Mark