https://number.subwiki.org/w/index.php?title=Chen_prime&feed=atom&action=history Chen prime - Revision history 2022-08-15T06:53:20Z Revision history for this page on the wiki MediaWiki 1.24alpha https://number.subwiki.org/w/index.php?title=Chen_prime&diff=522&oldid=prev Vipul: Created page with '{{prime number property}} ==Definition== A '''Chen prime''' is a prime number [itex]p[/itex] such that [itex]p + 2[/itex] is either a prime number or is a semiprime, i.…' 2010-05-03T20:31:55Z <p>Created page with &#039;{{prime number property}} ==Definition== A &#039;&#039;&#039;Chen prime&#039;&#039;&#039; is a <a href="/wiki/Prime_number" title="Prime number">prime number</a> &lt;math&gt;p&lt;/math&gt; such that &lt;math&gt;p + 2&lt;/math&gt; is either a prime number or is a <a href="/wiki/Semiprime" title="Semiprime">semiprime</a>, i.…&#039;</p> <p><b>New page</b></p><div>{{prime number property}}<br /> <br /> ==Definition==<br /> <br /> A '''Chen prime''' is a [[prime number]] &lt;math&gt;p&lt;/math&gt; such that &lt;math&gt;p + 2&lt;/math&gt; is either a prime number or is a [[semiprime]], i.e., a product of two primes.<br /> <br /> The smaller member of any pair of [[twin primes]] is a Chen prime.<br /> <br /> ==Occurrence==<br /> <br /> ===Initial values===<br /> <br /> {{oeis|A109611}}<br /> <br /> The first few Chen primes are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 47, 53, 59, 67, 71, 83, 89, 101, 107, 109, 113, 127, 131, 137, 139, 149, 157, 167, 179, 181, 191, 197, 199, 211, 227, 233, 239, 251, 257, 263, 269, 281, 293, 307, 311, 317, 337, 347, 353, 359, 379, 389, 401, 409.<br /> <br /> The smallest primes that are ''not'' Chen primes are: 43, 61, 73, 79, 97.<br /> <br /> ===Proportion of primes===<br /> <br /> {| class=&quot;wikitable&quot; border=&quot;1&quot;<br /> ! &lt;math&gt;n&lt;/math&gt; !! Number of primes &lt;math&gt;\le n&lt;/math&gt; !! Number of Chen primes &lt;math&gt;\le n&lt;/math&gt; !! Proportion of primes that are Chen primes<br /> |-<br /> | 10 || 4 || 4 || 1<br /> |-<br /> | 100 || 25 || 20 || &lt;math&gt;4/5 = 0.8&lt;/math&gt;<br /> |-<br /> | 1000 || 168 || ? || ?<br /> |}<br /> <br /> ==Relation with other properties==<br /> <br /> ===Properties for pairs===<br /> <br /> {| class=&quot;wikitable&quot; border=&quot;1&quot;<br /> ! Property !! Meaning !! Comment<br /> |-<br /> | [[twin primes]] || primes &lt;math&gt;p&lt;/math&gt; and &lt;math&gt;p + 2&lt;/math&gt; || the lower member of a pair of twin primes is always a Chen prime. The converse doesn't hold, with the smallest counterexample being &lt;math&gt;(7,9)&lt;/math&gt;.<br /> |}</div> Vipul