Having helped Lou Franco in his effort to parallelize primes computation and solved the fourth question of Google Treasure Hunt using Clojure, I thought I knew pretty well how to produce primes in Clojure but I stumbled accross some Haskell code that was far smarter. Here it is, now ported to Clojure:

(def primes (lazy-cons 2 ((fn this[n]

(let [potential-divisors (take-while #(<= (* % %) n) primes)]

(if (some #(zero? (rem n %)) potential-divisors)

(recur (inc n))

(lazy-cons n (this (inc n)))))) 3)))

*No, no, no!*I was plain wrong: if I need to seed with

**Update:**In comments, Cale Gibbard points out that my definition of prime numbers is loose: 1 isn't a prime. I fixed the code.

## 3 comments:

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.

@squeegee: thanks for the link to this interesting paper.

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)))

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