User:WillNess
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A perpetual Haskell newbie. I like this semioneliner:
 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
foldi
is on Treelike folds page. union
and more at Prime numbers.
The constructive definition of primes is the Sieve of Eratosthenes:
using standard definition
 . . . or, :) :) .
Trial division sieve is:
If you're put off by selfreferentiality, just replace or on the righthand side of equations with , but even ancient Greeks knew better.