Generators/iterators, Pythonicity, and primes
Arnaud Delobelle
arnodel at googlemail.com
Sat Apr 11 23:26:05 CEST 2009
John Posner <jjposner at snet.net> writes:
> 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
You could do something like this with the help of itertools.ifilter:
prime_gen = ifilter(
lambda n, P=[]: all(n%p for p in P) and not P.append(n),
count(2)
)
I omitted the 'if p <= sqrt(n)' as it doesn't help the generator go
faster. You could use itertools.takewhile for that:
prime_gen = ifilter(
lambda n, P=[]:
all(n%p for p in takewhile(lambda p, s=n**0.5: p<=s, P))
and not P.append(n),
count(2)
)
Of course there is no excuse for writing Python like that :)
--
Arnaud
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