# User:WillNess

### From HaskellWiki

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::::<math>\textstyle\mathbb{S} = \mathbb{N}_{2} \setminus \bigcup_{p\in \mathbb{S}} \{n p:n \in \mathbb{N}_{p}\}</math> |
::::<math>\textstyle\mathbb{S} = \mathbb{N}_{2} \setminus \bigcup_{p\in \mathbb{S}} \{n p:n \in \mathbb{N}_{p}\}</math> |
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where |
where |
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::::<math>\textstyle\mathbb{N}_{k} = \{ n \in \mathbb{N} : n \geq k \}</math>   . . . or,  <math>\textstyle\mathbb{N}_{k} = \{k\} \bigcup \mathbb{N}_{k+1}</math>   :) :) . |
::::<math>\textstyle\mathbb{N}_{k} = \{ n \in \mathbb{N} : n \geq k \}</math>   . . . or,  <math>\textstyle\mathbb{N}_{k} = \{k\} \bigcup \mathbb{N}_{k+1}</math>   :) :) . |
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Trial division sieve: |
Trial division sieve: |
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− | ::::<math>\textstyle\mathbb{T} = \{n \in \mathbb{N}_{2}: (\not\exists p \in \mathbb{T}) (p\leq \sqrt{n}\,, p\mid n)\}</math> |
+ | ::::<math>\textstyle\mathbb{T} = \{n \in \mathbb{N}_{2}: (\forall p \in \mathbb{T})(2\leq p\leq \sqrt{n}\, \Rightarrow \neg{(p \mid n)})\}</math> |

If you're put off by self-referentiality, just replace <math>\mathbb{S}</math> or <math>\mathbb{T}</math> on the right-hand side of equations with <math>\mathbb{N}_{2}</math>. |
If you're put off by self-referentiality, just replace <math>\mathbb{S}</math> or <math>\mathbb{T}</math> on the right-hand side of equations with <math>\mathbb{N}_{2}</math>. |

## Revision as of 18:42, 5 September 2011

I'm interested in Haskell.

I like *this*:

-- 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]) gaps k s@(c:t) | k < c = k : gaps (k+2) s -- minus [k,k+2..] (c:t), k<=c | True = gaps (k+2) t -- fused to avoid a space leak fix g = xs where xs = g xs -- global defn to avoid space leak

`foldi`

is on Tree-like folds page. `union`

and more at Prime numbers.

The math formula for Sieve of Eratosthenes,

where

- . . . or, :) :) .

Trial division sieve:

If you're put off by self-referentiality, just replace or on the right-hand side of equations with .