https://number.subwiki.org/w/index.php?title=Euclid_prime&feed=atom&action=history Euclid prime - Revision history 2022-05-17T21:47:20Z Revision history for this page on the wiki MediaWiki 1.24alpha https://number.subwiki.org/w/index.php?title=Euclid_prime&diff=274&oldid=prev Vipul: Created page with '{{prime number property}} ==Definition== A ''Euclid prime''' is a prime number that is one more than a defining ingredient::primorial. In other words, it is a prime num...' 2009-04-30T21:17:40Z <p>Created page with &#039;{{prime number property}} ==Definition== A &#039;&#039;Euclid prime&#039;&#039;&#039; is a <a href="/wiki/Prime_number" title="Prime number">prime number</a> that is one more than a <a href="/w/index.php?title=Defining_ingredient::primorial&amp;action=edit&amp;redlink=1" class="new" title="Defining ingredient::primorial (page does not exist)">defining ingredient::primorial</a>. In other words, it is a prime num...&#039;</p> <p><b>New page</b></p><div>{{prime number property}}<br /> <br /> ==Definition==<br /> <br /> A ''Euclid prime''' is a [[prime number]] that is one more than a [[defining ingredient::primorial]]. In other words, it is a prime number of the form &lt;math&gt;k\# + 1&lt;/math&gt;, where &lt;math&gt;k\#&lt;/math&gt; denotes the product of the first &lt;math&gt;k&lt;/math&gt; primes.<br /> <br /> A natural number of the form &lt;math&gt;k\#+ 1&lt;/math&gt; is termed a [[defining ingredient::Euclid number]], so a Euclid prime is a Euclid number that happens to be prime.<br /> <br /> ==Occurrence==<br /> <br /> {{oeis|A018239}}<br /> <br /> ===Initial values===<br /> <br /> The initial values of Euclid numbers are prime. For &lt;math&gt;k=0,1,2,3,4,5&lt;/math&gt;, the corresponding Euclid numbers &lt;math&gt;2,3,7,31,211,2311&lt;/math&gt; are prime. The first Euclid number that is not prime is &lt;math&gt;30031&lt;/math&gt;, corresponding to &lt;math&gt;k = 6&lt;/math&gt;.</div> Vipul