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Primality.html
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<!DOCTYPE html>
<html>
<head>
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<!-- TITLE AND CUSTOM CSS -->
<title> Title </title>
<link rel="stylesheet" href="css/primetest.css">
</head>
<body>
<div class="header">
<h1 style="color: white"><b>Algorithms</b></h1>
<p style="color: white">Bubble Sort</p>
</div>
<div class="topnav">
<div id="mySidenav" class="sidenav">
<a href="javascript:void(0)" class="closebtn" onclick="closeNav()">←</a>
<a href="https://www.amazon.com/s/ref=nb_sb_noss_2/144-7551219-7280505?url=search-alias%3Daps&field-keywords=number+theory">Shop</a>
<a href='#'>Books</a>
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Primes
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</button>
<div class="dropdown-content">
<a href="Primality.html">Introduction</a>
<a href="PrimeFact.html">Prime Factors</a>
<a href="RSA.html">RSA Encryption</a>
</div>
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Modular Arithmetic
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<a href="welcome.html">Introduction</a>
<a href="ModularAddMulSub.html">Modular Arithmetic</a>
<a href="congo.html">Modular Congruency</a>
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Algorithms
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<h2><span style="margin-left: 400px"><b>Primes</b></span></h2>
<h3 style="font-family: Raleway">Introduction To Primes</h3>
<p style="font-size: 18px">In Number theory, Primes play a very important role. They are the <b><i>keys</i></b> of Code and Cryptography.
<br> Fist time we used Primes was in the Problem of <a href="PrimeFact.html"><b><i>factorisation</i></b></a>.</p>
<p style="font-size: 18px">They can only be divided by 1 or Themselves;
<br> That's why we call them <b><i>Primes</i></b>.</p>
<br>
<br>
<h2 style="font-family: Merriweather">Examples With Visualisation</h2>
<p style="font-size: 25px">Primes as Locks :</p>
<div style="margin-left: 65px"><img src="css//img//05f1d72b048ebba84dc96e1e6f02ba29ccd88457.png"></div>
<br>
<p style="font-size: 18px">As you can see in the above explanation, Primes are the builing blocks of any natural number.</p>
<p style="font-size: 18px">For example, if we take any two large Prime numbers, say <b>P1</b> = 709 and <b>P2 </b>= 733
<br> their product, i.e. <b>P1</b>*<b>P2</b> = <b>519697</b>....
<br> that was easy, we could just use a calculator for that, <b>but</b> ;
<br> if I ask you to find two primes that multiply to give 519697 as a product,
<br> then its difficult, right ?!
<br>
</p>
<p>Well, its not your fault, there are limits to our calculation prowess and we accept it. In the case of Large Primes, Brute Force gets increasingly difficult. Here is an example of that : </p>
<div style="margin-left: 200px"><img src="css//img//9df89f48e72c47c84170f183477b5c1628307785.png"></div>
<p> As you can see Time increases exponentially as the size of input increases.</p>
<p> But how can we check if a number is Prime or not .....
<br> Well we have a tool for that; Check the below section.</p>
<p style="padding-left: 800px;font-size: 10px"><i>Source : KhanAcademy.com</i></p>
</div>
<div class="card">
<h2>Primality Checker</h2>
<br>
<br>
<div style="margin-left: 250px">
<form>
<input type="number" id="data" placeholder="Enter the number" required>
</form>
<br>
<p>
<button style="margin-left: 50px" class="button" onclick="res()">Check</button>
<p id="ans" style="font-family: Merriweather;margin-left: 100px"><b></b></p>
</div>
</div>
</div>
<div class="sticky">
<div class="card">
<h2 style="font-family: Merriweather">References</h2>
<div>
<a href="https://ocw.mit.edu/courses/mathematics/18-785-number-theory-i-fall-2016/"><img src="css//img//mitocw_1024x768.jpg" alt="mitocw" style="height: 200px ; width: 200px"></a>
</div>
<p>MIT OpenCourseWare By Prof.Andrew Sutherland</p>
<a href="https://ocw.mit.edu/courses/mathematics/18-785-number-theory-i-fall-2016/">
<button class="button" id="mit"><span>Visit </span></button>
</a>
</div>
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