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    <p>Question:</p> <blockquote> <p>Find the sum of all the primes below two million.</p> </blockquote> <p>It's a simple <a href="http://en.wikipedia.org/wiki/Sieve_of_Eratosthenes" rel="nofollow noreferrer">sieve</a>. You should read about it but the general idea is to iterate over each number - if the value at index number is <code>0</code>, it's prime and you mark off multiples of that number (since all those multiples <em>must not</em> be prime). Ignore if it's <code>1</code> (composite). I'll provide some comments to explain what this code in particular is doing,</p> <pre><code>marked = [0] * 2000000 # &lt;- just set up the list value = 3 # &lt;- starting at 3 then checking only odds s = 2 # &lt;- BUT include 2 since its the only even prime while value &lt; 2000000: if marked[value] == 0: # &lt;- if number at index value is 0 it's prime s += value # so add value to s (the sum) i = value # &lt;- now mark off future numbers that are multiples of while i &lt; 2000000: # value up until 2mil marked[i] = 1 # &lt;- number @ index i is a multiple of value so mark i += value # &lt;- increment value each time (looking for multiples) value += 2 # &lt;- only check every odd number print s </code></pre> <p>Two optimizations for this code:</p> <ol> <li>The initial value of <code>i</code> could be set to <code>value*value</code> == <code>value**2</code></li> <li>Could easily change this to use a list of length 1 million since we already know no evens are primes</li> </ol> <p><strong>EDIT:</strong></p> <p>While I hope my answer helps explain operations of sieves for future visitors, if you are looking for <em>a very fast sieve implementation</em> please refer to <a href="https://stackoverflow.com/questions/2068372/fastest-way-to-list-all-primes-below-n-in-python">this question</a>. Great performance analysis by unutbu and some excellent algorithms posted by Robert William Hanks!</p>
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    1. POExplanation needed for sum of prime below n numbers
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    1. COCan you please check my code and tell me whether its like sieve or not.
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    2. COThanks, I re-factored my code and now it can show result within in 2 sec which was efficient than lassevk's program :D.
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