To: Kermit Rose

Subject: Re: Some philosophy about prime numbers

--- In primenumbers@yahoogroups.com, "Kermit Rose" <kermit@p...> wrote:

> "There is no formula that produces all primes and ONLY primes."

>

> Does anyone disagree with this statement?

From: JRenze

Date: 12/19/05 18:21:19

Yes, I disagree. See http://functions.wolfram.com/13.03.06.0009.01 or

http://mathworld.wolfram.com/PrimeFormulas.html Equations (13) and (14).

This is a formula which for positive integer input n returns the nth

prime. It is not recursive and no primes or number theoretic

functions explicitly appear on the right hand side.

John

From Kermit Rose

You show an interesting formula. It clearly shows that it's possible to

cast a simple iterative algorithm

into a formula by using the summation notation.

Thus you show us that the summation notation blurs the distinction between

a non-recursive algorithm and a

simple formula.