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<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="39_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:39_1"/><i><font color="Green">E38</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">n</font> &amp; <font color="Maroon">n</font> <a href="binop_2.html#K24">*</a> <font color="Maroon">n</font> <a href="xxreal_0.html#R1">&lt;=</a> 83 &amp; <font color="Maroon">n</font> is <a href="int_2.html#V1">prime</a> )
 ;<br/><a NAME="E2:39_1"/>
83 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">2 <a href="binop_2.html#K24">*</a> 41</span>)</span> <a href="binop_2.html#K23">+</a> 1
 ;<br/><a NAME="E3:39_1"/><b>then </b><i><font color="Green">E39</font></i>: 
not 2 <a href="nat_1.html#R1">divides</a> 83
 <b>by </b><i/>;<br/><a NAME="E4:39_1"/>
83 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">3 <a href="binop_2.html#K24">*</a> 27</span>)</span> <a href="binop_2.html#K23">+</a> 2
 ;<br/><a NAME="E5:39_1"/><b>then </b><i><font color="Green">E40</font></i>: 
not 3 <a href="nat_1.html#R1">divides</a> 83
 <b>by </b><i/>;<br/><a NAME="E6:39_1"/>
83 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">5 <a href="binop_2.html#K24">*</a> 16</span>)</span> <a href="binop_2.html#K23">+</a> 3
 ;<br/><a NAME="E7:39_1"/><b>then </b><i><font color="Green">E46</font></i>: 
not 5 <a href="nat_1.html#R1">divides</a> 83
 <b>by </b><i/>;<br/><a NAME="E8:39_1"/>
83 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">7 <a href="binop_2.html#K24">*</a> 11</span>)</span> <a href="binop_2.html#K23">+</a> 6
 ;<br/><a NAME="E9:39_1"/><b>then </b><i><font color="Green">E47</font></i>: 
not 7 <a href="nat_1.html#R1">divides</a> 83
 <b>by </b><i/>;<br/><a NAME="E10:39_1"/>
83 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">11 <a href="binop_2.html#K24">*</a> 7</span>)</span> <a href="binop_2.html#K23">+</a> 6
 ;<br/><a NAME="E11:39_1"/><b>then </b><i><font color="Green">E48</font></i>: 
not 11 <a href="nat_1.html#R1">divides</a> 83
 <b>by </b><i/>;<br/><a NAME="E12:39_1"/>
83 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">13 <a href="binop_2.html#K24">*</a> 6</span>)</span> <a href="binop_2.html#K23">+</a> 5
 ;<br/><a NAME="E13:39_1"/><b>then </b><i><font color="Green">E53</font></i>: 
not 13 <a href="nat_1.html#R1">divides</a> 83
 <b>by </b><i/>;<br/><a NAME="E14:39_1"/>
83 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">17 <a href="binop_2.html#K24">*</a> 4</span>)</span> <a href="binop_2.html#K23">+</a> 15
 ;<br/><a NAME="E15:39_1"/><b>then </b><i><font color="Green">E54</font></i>: 
not 17 <a href="nat_1.html#R1">divides</a> 83
 <b>by </b><i/>;<br/><a NAME="E16:39_1"/>
83 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">19 <a href="binop_2.html#K24">*</a> 4</span>)</span> <a href="binop_2.html#K23">+</a> 7
 ;<br/><a NAME="E17:39_1"/><b>then </b><i><font color="Green">E55</font></i>: 
not 19 <a href="nat_1.html#R1">divides</a> 83
 <b>by </b><i/>;<br/><a NAME="E18:39_1"/>
83 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">23 <a href="binop_2.html#K24">*</a> 3</span>)</span> <a href="binop_2.html#K23">+</a> 14
 ;<br/><a NAME="E19:39_1"/><b>then </b>
not 23 <a href="nat_1.html#R1">divides</a> 83
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E20:39_1"/>
not <font color="Maroon">n</font> <a href="nat_1.html#R1">divides</a> 83
 <b>by </b><i><a class="txt" href="nat_4.html#E1:39_1"><i><font color="Green">E38</font></i></a>, <a class="txt" href="nat_4.html#E3:39_1"><i><font color="Green">E39</font></i></a>, <a class="txt" href="nat_4.html#E5:39_1"><i><font color="Green">E40</font></i></a>, <a class="ref" href="nat_4.html#T2" target="_self">Th2</a>, <a class="ref" href="nat_4.html#T3" target="_self">Th3</a>, , , , <a class="txt" href="nat_4.html#E7:39_1"><i><font color="Green">E46</font></i></a>, </i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:39"/>
83 is <a href="int_2.html#V1">prime</a>
 <b>by </b><i/>;<br/>


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