# Pierpont primes

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 http://en.wikipedia.org/wiki/Pierpont_prime

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.

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.

Any pointers are much appreciated.

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Here's a tip: work out the first few Pierpont Primes on a computer and then type them into the Online Encyclopedia of Integer Sequences and see what that gives you. – Kevin Buzzard Nov 5 '10 at 19:33
They are in OEIS: A005109 – Thomas S Nov 5 '10 at 19:49
Well mathematians are a pedantic bunch. If there had been several recent breakthroughs regarding Pierpont primes then two very natural places that people would update are OEIS and Wikipedia... – Kevin Buzzard Nov 5 '10 at 22:08
PS seems to me that the wikipedia page contains several recent results... – Kevin Buzzard Nov 5 '10 at 22:11
@Kevin: The recent results listed are about the geometric connections; I am interested in the distribution. Do the geometric results tell you anything about their distribution? Also, I was hoping that someone might point me to general results about primes p with p-1 being smooth. (Or at least, p-1 having many small factors.) Thanks for your input. – Thomas S Nov 6 '10 at 13:35