10x10 html table

tkoz0 · Jun 15, 2024 · 010961a · 010961a
1 parent a0b9565
commit 010961a
Showing 1 changed file with 44 additions and 2 deletions.
diff --git a/academic/misc/2024-math-calendar.html b/academic/misc/2024-math-calendar.html
@@ -356,8 +356,8 @@ <h1>Math Calendar 2024</h1>
         <td><a href="#jun11">11</a></td>
         <td><a href="#jun12">12</a></td>
         <td><a href="#jun13">13</a></td>
-        <td>14</td>
-        <td>15</td>
+        <td><a href="#jun14">14</a></td>
+        <td><a href="#jun15">15</a></td>
         <td>16</td>
     </tr>
     <tr>
@@ -5172,6 +5172,48 @@ <h3 id="jun13">Jun 13</h3>
 we would get 3138428376721, which clearly is 13 digits.
 </p>
 
+<h3 id="jun14">Jun 14</h3>
+
+\[{a+x\over ax}={1\over10},\quad{x\over a}={2\over 5}\]
+
+<p>
+We must have \(a\neq0\). Cross multiply to find \(10a+10x=ax\) and \(5x=2a\).
+Using the 2nd of these to substitute into the first, we have
+\(ax=10a+2\cdot2a=14a\Rightarrow x=14\).
+</p>
+
+<h3 id="jun15">Jun 15</h3>
+
+<p>
+How many twin primes are less than 100?
+</p>
+
+<p>
+The simplest way to solve this is probably thet sieve of Eratosthenes. We only
+need to cross out multiples of \(2,3,5,7\) since those are the only primes up
+to \(\sqrt{100}\). The table below has the primes in green, created as if
+starting entirely in green and then marking composite numbers in red.
+</p>
+
+<table>
+    <tr><td></td><td></td><td style="background:#7f7">2</td><td style="background:#7f7">3</td><td style="background:#f77">4</td><td style="background:#7f7">5</td><td style="background:#f77">6</td><td style="background:#7f7">7</td><td style="background:#f77">8</td><td style="background:#f77">9</td></tr>
+    <tr><td style="background:#f77">10</td><td style="background:#7f7">11</td><td style="background:#f77">12</td><td style="background:#7f7">13</td><td style="background:#f77">14</td><td style="background:#f77">15</td><td style="background:#f77">16</td><td style="background:#7f7">17</td><td style="background:#f77">18</td><td style="background:#7f7">19</td></tr>
+    <tr><td style="background:#f77">20</td><td style="background:#f77">21</td><td style="background:#f77">22</td><td style="background:#7f7">23</td><td style="background:#f77">24</td><td style="background:#f77">25</td><td style="background:#f77">26</td><td style="background:#f77">27</td><td style="background:#f77">28</td><td style="background:#7f7">29</td></tr>
+    <tr><td style="background:#f77">30</td><td style="background:#7f7">31</td><td style="background:#f77">32</td><td style="background:#f77">33</td><td style="background:#f77">34</td><td style="background:#f77">35</td><td style="background:#f77">36</td><td style="background:#7f7">37</td><td style="background:#f77">38</td><td style="background:#f77">39</td></tr>
+    <tr><td style="background:#f77">40</td><td style="background:#7f7">41</td><td style="background:#f77">42</td><td style="background:#7f7">43</td><td style="background:#f77">44</td><td style="background:#f77">45</td><td style="background:#f77">46</td><td style="background:#7f7">47</td><td style="background:#f77">48</td><td style="background:#f77">49</td></tr>
+    <tr><td style="background:#f77">50</td><td style="background:#f77">51</td><td style="background:#f77">52</td><td style="background:#7f7">53</td><td style="background:#f77">54</td><td style="background:#f77">55</td><td style="background:#f77">56</td><td style="background:#f77">57</td><td style="background:#f77">58</td><td style="background:#7f7">59</td></tr>
+    <tr><td style="background:#f77">60</td><td style="background:#7f7">61</td><td style="background:#f77">62</td><td style="background:#f77">63</td><td style="background:#f77">64</td><td style="background:#f77">65</td><td style="background:#f77">66</td><td style="background:#7f7">67</td><td style="background:#f77">68</td><td style="background:#f77">69</td></tr>
+    <tr><td style="background:#f77">70</td><td style="background:#7f7">71</td><td style="background:#f77">72</td><td style="background:#7f7">73</td><td style="background:#f77">74</td><td style="background:#f77">75</td><td style="background:#f77">76</td><td style="background:#f77">77</td><td style="background:#f77">78</td><td style="background:#7f7">79</td></tr>
+    <tr><td style="background:#f77">80</td><td style="background:#f77">81</td><td style="background:#f77">82</td><td style="background:#7f7">83</td><td style="background:#f77">84</td><td style="background:#f77">85</td><td style="background:#f77">86</td><td style="background:#f77">87</td><td style="background:#f77">88</td><td style="background:#7f7">89</td></tr>
+    <tr><td style="background:#f77">90</td><td style="background:#f77">91</td><td style="background:#f77">92</td><td style="background:#f77">93</td><td style="background:#f77">94</td><td style="background:#f77">95</td><td style="background:#f77">96</td><td style="background:#7f7">97</td><td style="background:#f77">98</td><td style="background:#f77">99</td></tr>
+</table>
+
+<p>
+Next, count the primes \(p\) such that either \(p+2\) or \(p-2\) are prime. We
+find the primes \(3,5,7,11,13,17,19,29,31,41,43,59,61,71,73\). This list has 15
+primes.
+</p>
+
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