most recent 30 from http://mathoverflow.net 2013-05-23T15:18:51Z http://mathoverflow.net/feeds/question/44985 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/44985/pierpont-primes Thomas S 2010-11-05T19:03:56Z 2010-11-05T19:03:56Z

<p>A Pierpont prime is a prime $p$ that can be written as $$p=2^u 3^v + 1.$$ What is known about Pierpont primes? I'm not a number theorist, and the best I can find is <a href="http://en.wikipedia.org/wiki/Pierpont_prime" rel="nofollow">http://en.wikipedia.org/wiki/Pierpont_prime</a></p> <p>The few references given are all rather dated. Pierpont primes seem to have interesting connections to geometry. But again there are no references given. I'm interested in Pierpont primes because $\mathbb{Z}_p^\times$ has plenty of easy-to-find generators with smooth order.</p> <p>I would like to know that Pierpont primes are plentiful, as numerical evidence suggests. It seems that it is still open as to whether or not there are infinitely many.</p> <p>Any pointers are much appreciated.</p>