A perpetual Haskell newbie. I like this semi-one-liner:
-- inifinte folding idea due to Richard Bird -- double staged production idea due to Melissa O'Neill -- tree folding idea Dave Bayer / simplified formulation Will Ness primes = 2 : g (fix g) where g xs = 3 : gaps 5 (foldi (\(c:cs) -> (c:) . union cs)  [[x*x, x*x+2*x..] | x <- xs]) fix g = xs where xs = g xs -- global defn to avoid space leak gaps k s@(c:t) -- == minus [k,k+2..] (c:t), k<=c, | k < c = k : gaps (k+2) s -- fused to avoid a space leak | True = gaps (k+2) t
The constructive definition of primes is the Sieve of Eratosthenes:
using standard definition
- . . . or, :) :) .
Trial division sieve is:
If you're put off by self-referentiality, just replace or on the right-hand side of equations with , but even ancient Greeks knew better.