Euler has design of a homepage and there is a link back to the overview for each solution.

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-<h1 id="Euler-Problem-10">Euler Problem 10<a class="anchor-link" href="#Euler-Problem-10">&#182;</a></h1><p>The sum of the primes below 10 is 2 + 3 + 5 + 7 = 17.</p>
+<h1 id="Euler-Problem-10">Euler Problem 10<a class="anchor-link" href="#Euler-Problem-10">¶</a></h1><p><a href="/euler">Back to overview.</a></p><p>The sum of the primes below 10 is 2 + 3 + 5 + 7 = 17.</p>
 <p>Find the sum of all the primes below two million.</p>
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 <p>Okay, reuse prime generator from 7 and go.</p>
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 <div class=" highlight hl-ipython3"><pre><span></span><span class="kn">import</span> <span class="nn">timeit</span>

 <span class="k">def</span> <span class="nf">is_prime</span><span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="n">smaller_primes</span><span class="p">):</span>
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 <span class="k">assert</span><span class="p">(</span><span class="n">brute_force</span><span class="p">()</span> <span class="o">==</span> <span class="mi">142913828922</span><span class="p">)</span>
 <span class="nb">print</span><span class="p">(</span><span class="n">brute_force</span><span class="p">())</span>
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 <pre>61.8695481220002
 142913828922
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 <p>Okay, here it may actually be way smarter to use a sieve. We implent it because the old one was shitty. Okay, I am actually interested in the time difference. So we use the old one first and then implement the optimization.</p>
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 <div class=" highlight hl-ipython3"><pre><span></span><span class="k">def</span> <span class="nf">get_primes_smaller</span><span class="p">(</span><span class="n">number</span><span class="p">):</span>
    <span class="n">primes</span> <span class="o">=</span> <span class="p">[]</span>
    <span class="n">prospects</span> <span class="o">=</span> <span class="p">[</span><span class="n">n</span> <span class="k">for</span> <span class="n">n</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="n">number</span><span class="p">)]</span>
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 <span class="c1">#print(timeit.timeit(brute_force, number=1))</span>
 <span class="c1">#print(brute_force())</span>
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 <p>This did not even terminate. We optimize the sieve by stopping when $p^2 &gt; number$.</p>
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 <div class=" highlight hl-ipython3"><pre><span></span><span class="k">def</span> <span class="nf">sieve_of_eratosthenes</span><span class="p">(</span><span class="n">number</span><span class="p">):</span>
    <span class="n">primes</span> <span class="o">=</span> <span class="p">[]</span>
    <span class="n">prospects</span> <span class="o">=</span> <span class="p">[</span><span class="n">n</span> <span class="k">for</span> <span class="n">n</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="n">number</span><span class="p">)]</span>
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 <span class="k">assert</span><span class="p">(</span><span class="n">brute_force</span><span class="p">()</span> <span class="o">==</span> <span class="mi">142913828922</span><span class="p">)</span>
 <span class="nb">print</span><span class="p">(</span><span class="n">brute_force</span><span class="p">())</span>
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 <pre>74.5315607270004
 142913828922
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 <p>Okay, I honestly did not expect this to be slower than our generator. Gotta keep that in mind for future prime related problems.</p>
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