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    <p>The given code is not very efficient. Alternative solution (just as inefficient):<sup>&dagger;</sup></p> <pre><code>&gt;&gt;&gt; from math import sqrt &gt;&gt;&gt; def is_prime(n): ... return all(n % d for d in range(2, int(sqrt(n)) + 1)) ... &gt;&gt;&gt; def primes_up_to(n): ... return filter(is_prime, range(2, n)) ... &gt;&gt;&gt; list(primes_up_to(20)) [2, 3, 5, 7, 11, 13, 17, 19] </code></pre> <p>This code uses <a href="http://docs.python.org/3.1/library/functions.html#all" rel="nofollow noreferrer"><code>all</code></a>, <a href="http://docs.python.org/3.1/library/functions.html#range" rel="nofollow noreferrer"><code>range</code></a>, <a href="http://docs.python.org/3.1/library/functions.html#int" rel="nofollow noreferrer"><code>int</code></a>, <a href="http://docs.python.org/3.1/library/math.html#math.sqrt" rel="nofollow noreferrer"><code>math.sqrt</code></a>, <a href="http://docs.python.org/3.1/library/functions.html#filter" rel="nofollow noreferrer"><code>filter</code></a> and <a href="http://docs.python.org/3.1/library/functions.html#list" rel="nofollow noreferrer"><code>list</code></a>. It is not completely identical to your code, as it prints primes <em>up to</em> a certain number, not exactly <em>n</em> primes. For that, you can do:</p> <pre><code>&gt;&gt;&gt; from itertools import count, islice &gt;&gt;&gt; def n_primes(n): ... return islice(filter(is_prime, count(2)), n) ... &gt;&gt;&gt; list(n_primes(10)) [2, 3, 5, 7, 11, 13, 17, 19, 23, 29] </code></pre> <p>That introduces another two functions, namely <a href="http://docs.python.org/3.1/library/itertools.html#itertools.count" rel="nofollow noreferrer"><code>itertools.count</code></a> and <a href="http://docs.python.org/3.1/library/itertools.html#itertools.islice" rel="nofollow noreferrer"><code>itertools.islice</code></a>. (That last piece of code works only in Python 3.x; in Python 2.x, use <a href="http://docs.python.org/library/itertools.html#itertools.ifilter" rel="nofollow noreferrer"><code>itertools.ifilter</code></a> instead of <code>filter</code>.)</p> <hr> <p>&nbsp;&nbsp;<sup>&dagger;</sup>: A more efficient method is to use the <a href="http://en.wikipedia.org/wiki/Sieve_of_Eratosthenes" rel="nofollow noreferrer">Sieve of Eratosthenes</a>.</p>
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