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<feed xmlns="http://www.w3.org/2005/Atom"><title>Be My SpaceTime - prime</title><link href="https://avinal.space/" rel="alternate"></link><link href="https://avinal.space/feeds/prime.atom.xml" rel="self"></link><id>https://avinal.space/</id><updated>2021-01-09T22:29:00+05:30</updated><subtitle>눈치</subtitle><entry><title>Introduction to Prime Numbers</title><link href="https://avinal.space/posts/prime/prime1.html" rel="alternate"></link><published>2021-01-09T22:29:00+05:30</published><updated>2021-01-09T22:29:00+05:30</updated><author><name>Avinal</name></author><id>tag:avinal.space,2021-01-09:/posts/prime/prime1.html</id><summary type="html">&lt;p class="first last"&gt;A prime is a positive integer &lt;em&gt;p&lt;/em&gt; having exactly two positive divisors, namely &lt;em&gt;1&lt;/em&gt; and &lt;em&gt;p&lt;/em&gt;. An integer &lt;em&gt;n&lt;/em&gt; is composite if &lt;em&gt;n&lt;/em&gt; &amp;gt; &lt;em&gt;1&lt;/em&gt; and &lt;em&gt;n&lt;/em&gt; is not prime. (The number 1 is considered neither prime nor composite.)&lt;/p&gt;
</summary><content type="html">&lt;blockquote class="epigraph"&gt;
A prime is a positive integer &lt;em&gt;p&lt;/em&gt; having exactly two positive divisors, namely &lt;em&gt;1&lt;/em&gt; and &lt;em&gt;p&lt;/em&gt;. An integer &lt;em&gt;n&lt;/em&gt; is composite if &lt;em&gt;n&lt;/em&gt; &amp;gt; &lt;em&gt;1&lt;/em&gt; and &lt;em&gt;n&lt;/em&gt; is not prime. (The number 1 is considered neither prime nor composite.)&lt;/blockquote&gt;
&lt;p&gt;We can frame a brute force algorithm for checking primality of numbers using the above statement.&lt;/p&gt;
&lt;div class="highlight"&gt;&lt;pre&gt;&lt;span&gt;&lt;/span&gt;&lt;span class="kt"&gt;bool&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nf"&gt;is_prime&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;number&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;&lt;/span&gt;
&lt;span class="w"&gt;    &lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;factor&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&lt;span class="w"&gt;&lt;/span&gt;
&lt;span class="w"&gt;    &lt;/span&gt;&lt;span class="k"&gt;for&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;&amp;lt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;number&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;&lt;/span&gt;
&lt;span class="w"&gt;        &lt;/span&gt;&lt;span class="k"&gt;if&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;number&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;%&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;==&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;&lt;/span&gt;
&lt;span class="w"&gt;            &lt;/span&gt;&lt;span class="n"&gt;factor&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&lt;span class="w"&gt;&lt;/span&gt;
&lt;span class="w"&gt;        &lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;span class="w"&gt;&lt;/span&gt;
&lt;span class="w"&gt;    &lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;span class="w"&gt;&lt;/span&gt;
&lt;span class="w"&gt;    &lt;/span&gt;&lt;span class="k"&gt;return&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;factor&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;==&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="o"&gt;?&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nb"&gt;true&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;:&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nb"&gt;false&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&lt;span class="w"&gt;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;&lt;span class="w"&gt;&lt;/span&gt;
&lt;/pre&gt;&lt;/div&gt;
</content><category term="prime"></category><category term="prime"></category><category term="primenumbers"></category></entry></feed>