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    <p>Even if you succeed in taming the strange quadratic F# sequences design issues, there is certain algorithmic improvements still ahead. You are working in <code>(...((x-a)-b)-...)</code> manner here. <code>x</code>, or <code>around6</code>, is getting deeper and deeper, but it's the most frequently-producing sequence. <a href="http://www.haskell.org/haskellwiki/Prime_numbers#Linear_merging" rel="nofollow">Transform</a> it into <code>(x-(a+b+...))</code> scheme - or even use a tree structure to gain improvement in <em>complexity</em>. (sorry, that page is in Haskell). This gets actually very close to the complexity of imperative sieve, although still mush slower than the baseline C++ code. </p> <p>Measuring local <a href="http://en.wikipedia.org/wiki/Analysis_of_algorithms#Empirical_orders_of_growth" rel="nofollow">empirical orders of growth</a> as <code>O(n^a) &lt;--&gt; a = log(t_2/t_1) / log(n_2/n_1)</code> (<em>in <code>n</code> primes produced</em>), the ideal <code>n log(n) log(log(n))</code> translates into <code>O(n^1.12) .. O(n^1.085)</code> behaviour on <code>n=10^5..10^7</code> range. A simple C++ baseline <a href="http://ideone.com/fapob" rel="nofollow">imperative code</a> achieves <code>O(n^1.45 .. 1.18 .. 1.14)</code> while <a href="http://ideone.com/p0e81" rel="nofollow">tree-merging code</a>, as well as priority-queue based code, both exhibit steady <code>O(n^1.20)</code> behaviour, more or less. Of course C++ is ~<s>50</s><strong>20..15</strong> times faster, but that's mostly just a "constant factor". :)</p>
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    1. POGetting functional sieve of Eratosthenes fast
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    1. COYep, damn these constant factors. ;-) Unfortunately, although I really like functional, I have a hard time reading Haskell.
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    2. CO@primfaktor take a look [here](http://stackoverflow.com/a/8871918/849891), see if it helps in reading Haskell. If you know Prolog, see also my other [recent answer](http://stackoverflow.com/a/8882745/849891).
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    3. CO@primfaktor C++ is actually 20..15 times faster, I've just corrected it.
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