PAT/source/html/a1015.html

Reversible Primes
<div class="ques-view"><p>A <strong>reversible prime</strong> in any number system is a prime whose "reverse" in that number system is also a prime. For example in the decimal system 73 is a reversible prime because its reverse 37 is also a prime.</p>
<p>Now given any two positive integers <span class="katex"><span class="katex-mathml"><math><mrow><mi>N</mi></mrow>N</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.68333em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.10903em;">N</span></span></span></span> (<span class="katex"><span class="katex-mathml"><math><mrow><mo>&lt;</mo><mn>1</mn><msup><mn>0</mn><mn>5</mn></msup></mrow>&lt; 10^5</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.8141079999999999em;"></span><span class="strut bottom" style="height:0.853208em;vertical-align:-0.0391em;"></span><span class="base textstyle uncramped"><span class="mrel">&lt;</span><span class="mord mathrm">1</span><span class="mord"><span class="mord mathrm">0</span><span class="msupsub"><span class="vlist"><span style="top:-0.363em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span><span class="reset-textstyle scriptstyle uncramped mtight"><span class="mord mathrm mtight">5</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span>​</span></span></span></span></span></span></span>) and <span class="katex"><span class="katex-mathml"><math><mrow><mi>D</mi></mrow>D</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.68333em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.02778em;">D</span></span></span></span> (<span class="katex"><span class="katex-mathml"><math><mrow><mn>1</mn><mo>&lt;</mo><mi>D</mi><mo>≤</mo><mn>1</mn><mn>0</mn></mrow>1 &lt; D \le 10</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.8193em;vertical-align:-0.13597em;"></span><span class="base textstyle uncramped"><span class="mord mathrm">1</span><span class="mrel">&lt;</span><span class="mord mathit" style="margin-right:0.02778em;">D</span><span class="mrel">≤</span><span class="mord mathrm">1</span><span class="mord mathrm">0</span></span></span></span>), you are supposed to tell if <span class="katex"><span class="katex-mathml"><math><mrow><mi>N</mi></mrow>N</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.68333em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.10903em;">N</span></span></span></span> is a reversible prime with radix <span class="katex"><span class="katex-mathml"><math><mrow><mi>D</mi></mrow>D</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.68333em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.02778em;">D</span></span></span></span>.</p>
<h3 id="input-specification-">Input Specification:</h3>
<p>The input file consists of several test cases. Each case occupies a line which contains two integers <span class="katex"><span class="katex-mathml"><math><mrow><mi>N</mi></mrow>N</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.68333em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.10903em;">N</span></span></span></span> and <span class="katex"><span class="katex-mathml"><math><mrow><mi>D</mi></mrow>D</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.68333em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.02778em;">D</span></span></span></span>. The input is finished by a negative <span class="katex"><span class="katex-mathml"><math><mrow><mi>N</mi></mrow>N</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.68333em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.10903em;">N</span></span></span></span>.</p>
<h3 id="output-specification-">Output Specification:</h3>
<p>For each test case, print in one line <code>Yes</code> if <span class="katex"><span class="katex-mathml"><math><mrow><mi>N</mi></mrow>N</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.68333em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.10903em;">N</span></span></span></span> is a reversible prime with radix <span class="katex"><span class="katex-mathml"><math><mrow><mi>D</mi></mrow>D</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.68333em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.02778em;">D</span></span></span></span>, or <code>No</code> if not.</p>
<h3 id="sample-input-">Sample Input:</h3>
<pre><code class="lang-in">73 10
23 2
23 10
-2
</code></pre>
<h3 id="sample-output-">Sample Output:</h3>
<pre><code class="lang-out">Yes
Yes
No
</code></pre>
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