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<div class="header">
<div class="summary">
<a href="#func-members">Functions</a> </div>
<div class="headertitle">
<div class="title">primality_test.cpp File Reference</div> </div>
<div class="headertitle"><div class="title">primality_test.cpp File Reference</div></div>
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<div class="contents">
<p><a href="https://en.wikipedia.org/wiki/Primality_test">Primality test</a> implementation.
<p><a href="https://en.wikipedia.org/wiki/Primality_test" target="_blank">Primality test</a> implementation.
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;iostream&gt;</code><br />
</div><div class="textblock"><div class="dynheader">
@@ -107,7 +106,7 @@ Include dependency graph for primality_test.cpp:</div>
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</div><table class="memberdecls">
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="func-members" name="func-members"></a>
Functions</h2></td></tr>
<tr class="memitem:a2bfa6adead2bdcbf1dac94cbe08d7eaf"><td class="memItemLeft" align="right" valign="top">bool&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../da/d7b/primality__test_8cpp.html#a2bfa6adead2bdcbf1dac94cbe08d7eaf">IsPrime</a> (int number)</td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p><a href="https://en.wikipedia.org/wiki/Primality_test">Primality test</a> implementation. </p>
<p>A simple and efficient implementation of a function to test if a number is prime, based on the fact that </p><blockquote class="doxtable">
<p>Every Prime number, except 2 and 3, are of the form \(6k\pm1\) for integer values of k. </p>
<div class="textblock"><p ><a href="https://en.wikipedia.org/wiki/Primality_test" target="_blank">Primality test</a> implementation. </p>
<p >A simple and efficient implementation of a function to test if a number is prime, based on the fact that </p><blockquote class="doxtable">
<p >Every Prime number, except 2 and 3, are of the form \(6k\pm1\) for integer values of k. </p>
</blockquote>
<p>This gives a 3x speed improvement. </p>
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<a id="a2bfa6adead2bdcbf1dac94cbe08d7eaf"></a>
<a id="a2bfa6adead2bdcbf1dac94cbe08d7eaf" name="a2bfa6adead2bdcbf1dac94cbe08d7eaf"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a2bfa6adead2bdcbf1dac94cbe08d7eaf">&#9670;&nbsp;</a></span>IsPrime()</h2>
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<p>Check if a number is prime </p><dl class="params"><dt>Parameters</dt><dd>
<p >Check if a number is prime </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in]</td><td class="paramname">number</td><td>number to check </td></tr>
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<dl class="section return"><dt>Returns</dt><dd>true if prime else false </dd></dl>
<div class="fragment"><div class="line"><a name="l00018"></a><span class="lineno"> 18</span>&#160; {</div>
<div class="line"><a name="l00019"></a><span class="lineno"> 19</span>&#160; <span class="keywordflow">if</span> (((!(number &amp; 1)) &amp;&amp; number != 2) || (number &lt; 2) ||</div>
<div class="line"><a name="l00020"></a><span class="lineno"> 20</span>&#160; (number % 3 == 0 &amp;&amp; number != 3))</div>
<div class="line"><a name="l00021"></a><span class="lineno"> 21</span>&#160; <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a name="l00022"></a><span class="lineno"> 22</span>&#160; </div>
<div class="line"><a name="l00023"></a><span class="lineno"> 23</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> k = 1; 36 * k * k - 12 * k &lt; number; ++k) {</div>
<div class="line"><a name="l00024"></a><span class="lineno"> 24</span>&#160; <span class="keywordflow">if</span> ((number % (6 * k + 1) == 0) || (number % (6 * k - 1) == 0))</div>
<div class="line"><a name="l00025"></a><span class="lineno"> 25</span>&#160; <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a name="l00026"></a><span class="lineno"> 26</span>&#160; }</div>
<div class="line"><a name="l00027"></a><span class="lineno"> 27</span>&#160; <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
<div class="line"><a name="l00028"></a><span class="lineno"> 28</span>&#160;}</div>
<div class="fragment"><div class="line"><a id="l00018" name="l00018"></a><span class="lineno"> 18</span> {</div>
<div class="line"><a id="l00019" name="l00019"></a><span class="lineno"> 19</span> <span class="keywordflow">if</span> (((!(number &amp; 1)) &amp;&amp; number != 2) || (number &lt; 2) ||</div>
<div class="line"><a id="l00020" name="l00020"></a><span class="lineno"> 20</span> (number % 3 == 0 &amp;&amp; number != 3))</div>
<div class="line"><a id="l00021" name="l00021"></a><span class="lineno"> 21</span> <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a id="l00022" name="l00022"></a><span class="lineno"> 22</span> </div>
<div class="line"><a id="l00023" name="l00023"></a><span class="lineno"> 23</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> k = 1; 36 * k * k - 12 * k &lt; number; ++k) {</div>
<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span> <span class="keywordflow">if</span> ((number % (6 * k + 1) == 0) || (number % (6 * k - 1) == 0))</div>
<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span> <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span> }</div>
<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span> <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
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<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&nbsp;</a></span>main()</h2>
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<p>main function </p>
<div class="fragment"><div class="line"><a name="l00031"></a><span class="lineno"> 31</span>&#160; {</div>
<div class="line"><a name="l00032"></a><span class="lineno"> 32</span>&#160; <span class="comment">// Main Function</span></div>
<div class="line"><a name="l00033"></a><span class="lineno"> 33</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter the value of n to check if Prime\n&quot;</span>;</div>
<div class="line"><a name="l00034"></a><span class="lineno"> 34</span>&#160; <span class="keywordtype">int</span> n;</div>
<div class="line"><a name="l00035"></a><span class="lineno"> 35</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; n;</div>
<div class="line"><a name="l00036"></a><span class="lineno"> 36</span>&#160; <span class="keywordflow">if</span> (<a class="code" href="../../da/d7b/primality__test_8cpp.html#a2bfa6adead2bdcbf1dac94cbe08d7eaf">IsPrime</a>(n))</div>
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; n &lt;&lt; <span class="stringliteral">&quot; is Prime&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span>&#160; <span class="keywordflow">else</span></div>
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; n &lt;&lt; <span class="stringliteral">&quot; is not Prime&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a name="l00040"></a><span class="lineno"> 40</span>&#160; </div>
<div class="line"><a name="l00041"></a><span class="lineno"> 41</span>&#160; <span class="keywordflow">return</span> 0;</div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span>&#160;}</div>
<p >main function </p>
<div class="fragment"><div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</span> {</div>
<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span> <span class="comment">// Main Function</span></div>
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<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span> <span class="keywordtype">int</span> n;</div>
<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; n;</div>
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span> <span class="keywordflow">if</span> (<a class="code hl_function" href="../../da/d7b/primality__test_8cpp.html#a2bfa6adead2bdcbf1dac94cbe08d7eaf">IsPrime</a>(n))</div>
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; n &lt;&lt; <span class="stringliteral">&quot; is Prime&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span> <span class="keywordflow">else</span></div>
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; n &lt;&lt; <span class="stringliteral">&quot; is not Prime&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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<div class="ttc" id="abasic_istream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a></div></div>
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<div class="ttc" id="aendl_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a></div><div class="ttdeci">T endl(T... args)</div></div>
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