[Python-ideas] Is this PEP-able? for X in ListY while conditionZ:

[Joshua Landau]

On 2 July 2013 23:35, Greg Ewing <greg.ewing at canterbury.ac.nz> wrote:
> Oscar Benjamin wrote:
>>
>> def primes():
>>     primes_seen = []
>>     for n in count(2):
>>         if all(n % p for p in primes_seen):
>>             yield n
>>             primes_seen.append(n)
>>
>> This algorithm is actually even poorer as it doesn't stop at sqrt(n).
>
>
> Nor should it! When you're only dividing by primes, you
> can't stop at sqrt(n), you have to divide by *all* the
> primes less than n. Otherise you could miss a prime
> factor greater than sqrt(n) whose cofactor is not prime.

I'm not convinced.

Say you have 7 * 6. That is 7 * 3 * 2, so if 7 has a cofactor of 6
then 2 is a factor. The proof can be generalised.