Formula versus algorithm
- To: Kermit Rose
Subject: Re: Some philosophy about prime numbers
--- In email@example.com, "Kermit Rose" <kermit@p...> wrote:
> "There is no formula that produces all primes and ONLY primes."
> Does anyone disagree with this statement?
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.
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