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<h1>Introduction to Prime Numbers
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</h1>
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<li class="list-inline-item text-muted" title="2021-01-09T22:29:00+05:30">
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Sat 09 January 2021
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<a href="https://avinal.space/category/prime.html">prime</a>
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<a href="https://avinal.space/tag/prime.html">#prime</a>, <a href="https://avinal.space/tag/primenumbers.html">#primenumbers</a> </li>
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A prime is a positive integer <em>p</em> having exactly two positive divisors, namely <em>1</em> and <em>p</em>. An integer <em>n</em> is composite if <em>n</em> > <em>1</em> and <em>n</em> is not prime. (The number 1 is considered neither prime nor composite.)</blockquote>
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<p>We can frame a brute force algorithm for checking primality of numbers using the above statement.</p>
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<div class="highlight"><pre><span></span><span class="kt">bool</span><span class="w"> </span><span class="nf">is_prime</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">number</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"></span>
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<span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">factor</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"></span>
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<span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="n">number</span><span class="p">;</span><span class="w"> </span><span class="o">++</span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"></span>
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<span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">number</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"></span>
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<span class="w"> </span><span class="n">factor</span><span class="o">++</span><span class="p">;</span><span class="w"></span>
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<span class="w"> </span><span class="p">}</span><span class="w"></span>
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<span class="w"> </span><span class="p">}</span><span class="w"></span>
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<span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="n">factor</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span><span class="o">?</span><span class="w"> </span><span class="nb">true</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="nb">false</span><span class="p">;</span><span class="w"></span>
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<span class="p">}</span><span class="w"></span>
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</pre></div>
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