Generating Chen primes. - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-19T00:48:28Z http://mathoverflow.net/feeds/question/48087 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/48087/generating-chen-primes Generating Chen primes. Alex Botros 2010-12-02T19:59:51Z 2011-02-04T05:49:47Z <p>Let </p> <p><code>$A_p(n)=\#\{q&lt;n \vert \ qp-2 \ is \ prime\}$</code></p> <p>Where p,q are prime, n is an integer. My question is, it seems fairly reasonable to assume that for a fixed $n$, $A_p(n)$ can be bounded by a decreasing function, but can I prove it. Moreover, can it be shown that $\lim_{p \rightarrow \infty} A_p(n)=0$? Does anyone know of any work done on the subject?</p> http://mathoverflow.net/questions/48087/generating-chen-primes/54287#54287 Answer by Ergenheim for Generating Chen primes. Ergenheim 2011-02-04T05:08:54Z 2011-02-04T05:49:47Z <p>A powerful lead toward creating a proof can be found using the Croft Spiral Sieve:</p> <p>Note, referencing the Croft Spiral Sieve, that all squared primes are either mod30,1 or mod30,19. both of which have primes positioned in p-2 (at mod30,29 and mod30,17, respectively). To see why this is the case, first explore this: <a href="http://www.primesdemystified.com" rel="nofollow">http://www.primesdemystified.com</a>, in order to understand this: <a href="http://primesdemystified.com/ChordSequenceFactorizations.html" rel="nofollow">http://primesdemystified.com/ChordSequenceFactorizations.html</a></p>