I like this one-liner:
-- infinite folding due to Richard Bird -- double staged primes production due to Melissa O'Neill -- tree folding idea Heinrich Apfelmus / Dave Bayer primes = 2 : _Y ((3:) . gaps 5 . foldi (\(x:xs) -> (x:) . union xs)  . map (\p-> [p*p, p*p+2*p..])) _Y g = g (_Y g) -- multistage production via Y combinator gaps k s@(c:t) -- == minus [k,k+2..] (c:t), k<=c, | k < c = k : gaps (k+2) s -- fused for better performance | otherwise = gaps (k+2) t -- k==c
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.