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    <p>Tried to make a non-loop version just for fun. It came out like this:</p> <pre><code>def erathostenes(n): def helper_function(num_lst, acc): if not num_lst: return acc if len(num_lst) == 1: acc.append(num_lst[0]) return acc num = num_lst.pop(0) multiples = ([x for x in range(num + 1, num_lst[-1] + 1) if x % num == 0]) remains = ([x for x in num_lst if x not in multiples]) acc.append(num) return helper_function(remains, acc ) return helper_function(range(2, n + 1), []) </code></pre> <p>When i ran the timing, got 826 us for the post erathostenes(1000), and 26ms for my version (!!). Surprised me it was so slow.</p> <p>Functional programming it's more fun, but looks isn't the right fit for this problem, in Python (my guess is that it would be faster in a more functional language).</p> <p>So i tried a imperative version. It looks like this:</p> <pre><code>def erathostenes_imperative(n): limit = int(math.sqrt(n)) def helper_function(flags, size): for i in range(2,limit): if flags[i] == True: j = 2*i while j &lt; size: if j % i == 0: flags[j] = False j = j + i return [x for x in range(2, n + 1) if flags[x]] return helper_function([True]*(n + 1), n) </code></pre> <p>What i did was changing the list of integers into a list of True/False flags. Intuitively, looks like it's faster to iterate, right?</p> <p>My results where 831ms for erathostenes_imperative(100000), vs. 1.45 in your version.</p> <p>It's a shame that imperative writting it's faster. The code look so messy with all the fors, whiles, i's and j's</p>
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    1. POErathostenes sieve optimization
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    1. USLucas Ribeiro
    1. USLucas Ribeiro
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    1. COi'm not sure if your imperative version is totally correct. If you executed for n=10.000.000, the prime numbers should be 664579 and your version gives a result of 664580 (one more). Let's see if I can fix the problem. Thanks!
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      1. USAntoni
    2. COLol. Just edited, edited back not to spoil. Feel free to edit my post after you find the bug!
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      1. USLucas Ribeiro
 

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