Generators/iterators, Pythonicity, and primes

[Terry Reedy]

John Posner wrote:
> 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?

No.  You refer to the list being build in the code for building the list 
(very cute), which requires that the list be bound to a name at the 
start of the process rather than just when complete (which is never ;-).

tjr