Question

This is my code for finding primes using the Sieve of Eratosthenes.

list = [i for i in range(2, int(raw_input("Compute primes up to what number? "))+1)]  

for i in list:
    for a in list:
            if a!=i and a%i == 0:
                list.remove(a)

Trying to find a way to compress those nested for loops into some kind of generator or comprehension, but it doesn’t seem that you can apply a function to a list using a comprehension. I tried using map and filter, but I can’t seem to get it right.

Thinking about something like this:

print map(list.remove(a), filter(lambda a, i: (a%i ==0 and a!=i), [(a, i) for i in list for a in list])

Obviously doesn’t work for a dozen reasons. If I just was using the filter portion of that code:

filter(lambda a, i: (a%i ==0 and a!=i), **[(a, i) for i in list for a in list]**

What’s the proper way of putting two variables into the lambda? (a,i) makes it a tuple, but I want to submit ‘a’ and ‘i’ as independent variables to put into the lambda.

I ended up resolving the problem with this one-liner:

print sorted(set([i for i in range(2, int(raw_input("Compute primes up to what number? "))+1)]).difference(a for i in l for a in l if a!=i and a%i == 0))

Answer 1

It’s not precisely a direct translation of your loops, but it’s quite close and compact:

>>> l = range(2, 101)
>>> sorted(set(l).difference(a for i in l for a in l if a!=i and a%i == 0))
[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97]

Although I’d suggest a > i rather than a != 0 as being shorter and faster 😉