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<p>Reduced all possibilities of a number which cannot be prime. Eg: No even number, except 2 can be a prime number, hence we will increment our loop with i+2 jumping on all odd numbers only. If number is &lt;= 1 or if it is even except 2, break the loop and return false telling number is not prime.
<p>Reduced all possibilities of a number which cannot be prime. Eg: No even number, except 2 can be a prime number, hence we will increment our loop with i+6 jumping and check for i or i+2 to be a factor of the number; if it's a factor then we will return false otherwise true after the loop terminates at the terminating condition which is (i*i&lt;=num)
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;cassert&gt;</code><br />
<code>#include &lt;iostream&gt;</code><br />
@@ -111,12 +111,13 @@ Include dependency graph for check_prime.cpp:</div>
Functions</h2></td></tr>
<tr class="memitem:aa18b3517017d99bb4024853bddba5532"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:aa18b3517017d99bb4024853bddba5532"><td class="memTemplItemLeft" align="right" valign="top">bool&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../db/d93/check__prime_8cpp.html#aa18b3517017d99bb4024853bddba5532">is_prime</a> (T num)</td></tr>
<tr class="memdesc:aa18b3517017d99bb4024853bddba5532"><td class="mdescLeft">&#160;</td><td class="mdescRight">for IO operations <a href="../../db/d93/check__prime_8cpp.html#aa18b3517017d99bb4024853bddba5532">More...</a><br /></td></tr>
<tr class="separator:aa18b3517017d99bb4024853bddba5532"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../db/d93/check__prime_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p >Reduced all possibilities of a number which cannot be prime. Eg: No even number, except 2 can be a prime number, hence we will increment our loop with i+2 jumping on all odd numbers only. If number is &lt;= 1 or if it is even except 2, break the loop and return false telling number is not prime. </p>
<div class="textblock"><p >Reduced all possibilities of a number which cannot be prime. Eg: No even number, except 2 can be a prime number, hence we will increment our loop with i+6 jumping and check for i or i+2 to be a factor of the number; if it's a factor then we will return false otherwise true after the loop terminates at the terminating condition which is (i*i&lt;=num) </p>
<p >Copyright 2020 </p><dl class="section author"><dt>Author</dt><dd>omkarlanghe</dd></dl>
<p>A simple program to check if the given number if prime or not. </p>
</div><h2 class="groupheader">Function Documentation</h2>
@@ -137,32 +138,34 @@ template&lt;typename T &gt; </div>
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<p >Function to check if the given number is prime or not. </p><dl class="params"><dt>Parameters</dt><dd>
<p>for IO operations </p>
<p >for assert Function to check if the given number is prime or not. </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">num</td><td>number to be checked. </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>if number is prime, it returns @ true, else it returns @ false. </dd></dl>
<div class="fragment"><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="keywordtype">bool</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = <span class="keyword">true</span>;</div>
<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span> <span class="keywordflow">if</span> (num &lt;= 1) {</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> } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (num == 2) {</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>
<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span> } <span class="keywordflow">else</span> <span class="keywordflow">if</span> ((num &amp; 1) == 0) {</div>
<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"> 29</span> <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"> 30</span> }</div>
<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</span> <span class="keywordflow">if</span> (num &gt;= 3) {</div>
<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span> <span class="keywordflow">for</span> (T i = 3; (i * i) &lt;= (num); i = (i + 2)) {</div>
<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span> <span class="keywordflow">if</span> ((num % i) == 0) {</div>
<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = <span class="keyword">false</span>;</div>
<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span> <span class="keywordflow">break</span>;</div>
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span> }</div>
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span> }</div>
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span> }</div>
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span> <span class="keywordflow">return</span> (result);</div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span>}</div>
<div class="fragment"><div class="line"><a id="l00023" name="l00023"></a><span class="lineno"> 23</span> {</div>
<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span> <span class="keywordtype">bool</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = <span class="keyword">true</span>;</div>
<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span> <span class="keywordflow">if</span> (num &lt;= 1) {</div>
<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span> <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span> } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (num == 2 || num==3) {</div>
<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span> <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"> 29</span> } <span class="keywordflow">else</span> <span class="keywordflow">if</span> ((num%2) == 0 || num%3 == 0) {</div>
<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"> 30</span> <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<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="keywordflow">else</span> {</div>
<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span> <span class="keywordflow">for</span> (T i = 5; (i * i) &lt;= (num); i = (i + 6)) {</div>
<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span> <span class="keywordflow">if</span> ((num % i) == 0 || (num%(i+2)==0 )) {</div>
<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = <span class="keyword">false</span>;</div>
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span> <span class="keywordflow">break</span>;</div>
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span> }</div>
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span> }</div>
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span> }</div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span> <span class="keywordflow">return</span> (result);</div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span>}</div>
<div class="ttc" id="afibonacci__sum_8cpp_html_aadb40ac4c74a7efc0680b83eeee138aa"><div class="ttname"><a href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">math::fibonacci_sum::result</a></div><div class="ttdeci">uint64_t result(uint64_t n)</div><div class="ttdef"><b>Definition:</b> fibonacci_sum.cpp:76</div></div>
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</div>
@@ -183,26 +186,26 @@ template&lt;typename T &gt; </div>
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<p >Main function </p>
<div class="fragment"><div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span> {</div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span> <span class="comment">// perform self-test</span></div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span> assert(<a class="code hl_function" href="../../db/d93/check__prime_8cpp.html#aa18b3517017d99bb4024853bddba5532">is_prime</a>(50) == <span class="keyword">false</span>);</div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span> assert(<a class="code hl_function" href="../../db/d93/check__prime_8cpp.html#aa18b3517017d99bb4024853bddba5532">is_prime</a>(115249) == <span class="keyword">true</span>);</div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> </div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span> <span class="keywordtype">int</span> num = 0;</div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter the number to check if it is prime or not&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="l00052" name="l00052"></a><span class="lineno"> 52</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; num;</div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span> <span class="keywordtype">bool</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = <a class="code hl_function" href="../../db/d93/check__prime_8cpp.html#aa18b3517017d99bb4024853bddba5532">is_prime</a>(num);</div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span> <span class="keywordflow">if</span> (result) {</div>
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; num &lt;&lt; <span class="stringliteral">&quot; is a prime number&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="l00056" name="l00056"></a><span class="lineno"> 56</span> } <span class="keywordflow">else</span> {</div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; num &lt;&lt; <span class="stringliteral">&quot; is not a prime number&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="l00058" name="l00058"></a><span class="lineno"> 58</span> }</div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> </div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span>}</div>
<div class="fragment"><div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span> {</div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span> <span class="comment">// perform self-test</span></div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span> assert(<a class="code hl_function" href="../../db/d93/check__prime_8cpp.html#aa18b3517017d99bb4024853bddba5532">is_prime</a>(50) == <span class="keyword">false</span>);</div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> assert(<a class="code hl_function" href="../../db/d93/check__prime_8cpp.html#aa18b3517017d99bb4024853bddba5532">is_prime</a>(115249) == <span class="keyword">true</span>);</div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span> </div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> <span class="keywordtype">int</span> num = 0;</div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter the number to check if it is prime or not&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="l00053" name="l00053"></a><span class="lineno"> 53</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; num;</div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span> <span class="keywordtype">bool</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = <a class="code hl_function" href="../../db/d93/check__prime_8cpp.html#aa18b3517017d99bb4024853bddba5532">is_prime</a>(num);</div>
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span> <span class="keywordflow">if</span> (result) {</div>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; num &lt;&lt; <span class="stringliteral">&quot; is a prime number&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="l00057" name="l00057"></a><span class="lineno"> 57</span> } <span class="keywordflow">else</span> {</div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; num &lt;&lt; <span class="stringliteral">&quot; is not a prime number&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="l00059" name="l00059"></a><span class="lineno"> 59</span> }</div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> </div>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> <span class="keywordflow">return</span> 0;</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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<tr class="memdesc:db/d93/check__prime_8cpp"><td class="mdescLeft">&#160;</td><td class="mdescRight">Reduced all possibilities of a number which cannot be prime. Eg: No even number, except 2 can be a prime number, hence we will increment our loop with i+2 jumping on all odd numbers only. If number is &lt;= 1 or if it is even except 2, break the loop and return false telling number is not prime. <br /></td></tr>
<tr class="memdesc:db/d93/check__prime_8cpp"><td class="mdescLeft">&#160;</td><td class="mdescRight">Reduced all possibilities of a number which cannot be prime. Eg: No even number, except 2 can be a prime number, hence we will increment our loop with i+6 jumping and check for i or i+2 to be a factor of the number; if it's a factor then we will return false otherwise true after the loop terminates at the terminating condition which is (i*i&lt;=num) <br /></td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">file &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="d5/d67/complex__numbers_8cpp.html">complex_numbers.cpp</a></td></tr>
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<tr id="row_14_3_" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d5/df6/check__amicable__pair_8cpp.html" target="_self">check_amicable_pair.cpp</a></td><td class="desc">A C++ Program to check whether a pair of number is <a href="https://en.wikipedia.org/wiki/Amicable_numbers" target="_blank">amicable pair</a> or not </td></tr>
<tr id="row_14_4_" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d8/dd5/check__factorial_8cpp.html" target="_self">check_factorial.cpp</a></td><td class="desc">A simple program to check if the given number is a factorial of some number or not </td></tr>
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<tr id="row_14_7_" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d7/d89/double__factorial_8cpp.html" target="_self">double_factorial.cpp</a></td><td class="desc">Compute <a href="https://en.wikipedia.org/wiki/Double_factorial" target="_blank">double factorial</a>: \(n!!\) </td></tr>
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