Comments on: Primes http://clj-me.cgrand.net/2008/06/07/primes/ When the pupil is ready to learn, a teacher will appear. Tue, 07 Sep 2010 05:36:26 +0200 http://wordpress.org/?v=2.9.2 hourly 1 By: Cale Gibbard http://clj-me.cgrand.net/2008/06/07/primes/comment-page-1/#comment-5 Cale Gibbard Sun, 08 Jun 2008 19:41:00 +0000 http://clj-me.cgrand.net/2008/06/07/primes/#comment-5 Just thought I'd point out that 1 is by definition not a prime, since it has a multiplicative inverse (namely itself).<br/><br/>The following small tweak to the code avoids this:<br/><br/>(def primes (lazy-cat [2] ((fn this[n]<br/> (let [potential-divisors (take-while #(<= (* % %) n) primes)]<br/> (if (some #(zero? (rem n %)) (rest potential-divisors)) <br/> (recur (+ n 2))<br/> (lazy-cons n (this (+ n 2)))))) 3))) Just thought I’d point out that 1 is by definition not a prime, since it has a multiplicative inverse (namely itself).

The following small tweak to the code avoids this:

(def primes (lazy-cat [2] ((fn this[n]
(let [potential-divisors (take-while #(< = (* % %) n) primes)]
(if (some #(zero? (rem n %)) (rest potential-divisors))
(recur (+ n 2))
(lazy-cons n (this (+ n 2)))))) 3)))

]]> By: Christophe Grand http://clj-me.cgrand.net/2008/06/07/primes/comment-page-1/#comment-4 Christophe Grand Sun, 08 Jun 2008 08:20:00 +0000 http://clj-me.cgrand.net/2008/06/07/primes/#comment-4 @squeegee: thanks for the link to this interesting paper. @squeegee: thanks for the link to this interesting paper.

]]> By: squeegee http://clj-me.cgrand.net/2008/06/07/primes/comment-page-1/#comment-3 squeegee Sun, 08 Jun 2008 00:19:00 +0000 http://clj-me.cgrand.net/2008/06/07/primes/#comment-3 Very cool. I found some more discussion in a paper: <a HREF="http://www.cs.hmc.edu/~oneill/papers/Sieve-JFP.pdf" REL="nofollow">The Genuine Sieve of Eratosthenes (pdf)</a>. I've put up an implementation in clojure-contrib in the file <a HREF="http://clojure-contrib.svn.sourceforge.net/viewvc/clojure-contrib/trunk/lazy-seqs.clj?view=markup" REL="nofollow">lazy-seqs.clj</a> that borrows ideas from your blog post and the paper (and gives references to them). Performance averaged over the first 100,000 primes is about 206 microseconds per prime on a 2.16 GHz Core Duo. Very cool. I found some more discussion in a paper: The Genuine Sieve of Eratosthenes (pdf). I’ve put up an implementation in clojure-contrib in the file lazy-seqs.clj that borrows ideas from your blog post and the paper (and gives references to them). Performance averaged over the first 100,000 primes is about 206 microseconds per prime on a 2.16 GHz Core Duo.

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