blocks|key|1522600|text|我通过使用并发处理来解决这个问题。|type|unstyled|depth|inlineStyleRanges|entityRanges|data|1522601|Source|offset|length|1522602|entityMap|0|LINK|mutability|MUTABLE|url|http://web.archive.org/web/20080911213200/http://refactormycode.com/codes/471-experimental-prime-number-generator^0|0|0|6|0|0^^$0|@$1|2|3|4|5|6|7|N|8|@]|9|@]|A|$]]|$1|B|3|C|5|6|7|O|8|@]|9|@$D|P|E|Q|1|R]]|A|$]]|$1|F|3|-4|5|6|7|S|8|@]|9|@]|A|$]]]|G|$H|$5|I|J|K|A|$L|M]]]]

I approached the problem by using concurrent processing.

<a href="http://web.archive.org/web/20080911213200/http://refactormycode.com/codes/471-experimental-prime-number-generator" rel="nofollow noreferrer">Source</a>

blocks|key|1522633|text|下面是一个简单(但不是非常快)的sieve实现：|type|unstyled|depth|inlineStyleRanges|entityRanges|data|1522634|-module(primes).
-export([sieve/1]).
-include_lib("eunit/include/eunit.hrl").

sieve([])+->
++++[];
sieve([H%7CT])+->++++++++++
++++List+=+lists:filter(fun(N)+->+N+rem+H+/=+0+end,+T),
++++[H%7Csieve(List)];
sieve(N)+->
++++sieve(lists:seq(2,N)).|code-block|syntax|javascript|1522635|entityMap^0|0|0^^$0|@$1|2|3|4|5|6|7|I|8|@]|9|@]|A|$]]|$1|B|3|C|5|D|7|J|8|@]|9|@]|A|$E|F]]|$1|G|3|-4|5|6|7|K|8|@]|9|@]|A|$]]]|H|$]]

Here's a simple (but not terribly fast) sieve implementation:

<pre><code>-module(primes).
-export([sieve/1]).
-include_lib("eunit/include/eunit.hrl").

sieve([]) -&gt;
 [];
sieve([H|T]) -&gt; 
 List = lists:filter(fun(N) -&gt; N rem H /= 0 end, T),
 [H|sieve(List)];
sieve(N) -&gt;
 sieve(lists:seq(2,N)).
</code></pre>

blocks|key|1737682|text|到目前为止，我最快的代码(比Andrea的更快)是使用array：|type|unstyled|depth|inlineStyleRanges|entityRanges|data|1737683|-module(seed4).
-export([get/1]).

get(N)+->+WorkList+=+array:new([{size,+N},+{default,+empty}]),
++++++++++get(2,+N,+WorkList,+[]).

get(thats_the_end,+_N,+_WorkList,+ResultList)+->+lists:reverse(ResultList);
get(CurrentPrime,+N,+WorkList,+ResultList)+->+ModWorkList+=+markAsPrime(CurrentPrime,+N,+WorkList),
++++++++++++++++++++++++++++++++++++++++++++++NextPrime+=+findNextPrime(CurrentPrime+%2B+1,+N,+WorkList),
++++++++++++++++++++++++++++++++++++++++++++++get(NextPrime,+N,+ModWorkList,+[CurrentPrime%7CResultList]).


markAsPrime(CurrentPrime,+N,+WorkList)+when+CurrentPrime+=<+N+->+WorkListMod+=+replace(CurrentPrime,+WorkList,+prime),
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++markAllMultiples(CurrentPrime,+N,+2*CurrentPrime,+WorkListMod).

markAllMultiples(_ThePrime,+N,+TheCurentMark,+WorkList)+when+TheCurentMark+>+N+->+WorkList;
markAllMultiples(ThePrime,+N,+TheCurrentMark,+WorkList)+->+WorkListMod+=+replace(TheCurrentMark,+WorkList,+marked),
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++markAllMultiples(ThePrime,+N,+TheCurrentMark+%2B+ThePrime,+WorkListMod).

findNextPrime(Iterator,+N,+_WorkList)+when+Iterator+>+N+->+thats_the_end;
findNextPrime(Iterator,+N,+WorkList)+->+I+=+array:get(Iterator+-+1,+WorkList),
++++++++++++++++++++++++++++++++++++++++if
++++++++++++++++++++++++++++++++++++++++++I+=:=+empty+->+Iterator;
++++++++++++++++++++++++++++++++++++++++++true+->+findNextPrime(Iterator+%2B+1,+N,+WorkList)
++++++++++++++++++++++++++++++++++++++++end.

replace(N,+L,+New)+->+array:set(N+-+1,+New,+L).|code-block|syntax|javascript|1737684|entityMap^0|0|0^^$0|@$1|2|3|4|5|6|7|I|8|@]|9|@]|A|$]]|$1|B|3|C|5|D|7|J|8|@]|9|@]|A|$E|F]]|$1|G|3|-4|5|6|7|K|8|@]|9|@]|A|$]]]|H|$]]

my fastest code so far (faster than Andrea's) is with using array:

<pre><code>-module(seed4).
-export([get/1]).

get(N) -&gt; WorkList = array:new([{size, N}, {default, empty}]),
 get(2, N, WorkList, []).

get(thats_the_end, _N, _WorkList, ResultList) -&gt; lists:reverse(ResultList);
get(CurrentPrime, N, WorkList, ResultList) -&gt; ModWorkList = markAsPrime(CurrentPrime, N, WorkList),
 NextPrime = findNextPrime(CurrentPrime + 1, N, WorkList),
 get(NextPrime, N, ModWorkList, [CurrentPrime|ResultList]).


markAsPrime(CurrentPrime, N, WorkList) when CurrentPrime =&lt; N -&gt; WorkListMod = replace(CurrentPrime, WorkList, prime),
 markAllMultiples(CurrentPrime, N, 2*CurrentPrime, WorkListMod).

markAllMultiples(_ThePrime, N, TheCurentMark, WorkList) when TheCurentMark &gt; N -&gt; WorkList;
markAllMultiples(ThePrime, N, TheCurrentMark, WorkList) -&gt; WorkListMod = replace(TheCurrentMark, WorkList, marked),
 markAllMultiples(ThePrime, N, TheCurrentMark + ThePrime, WorkListMod).

findNextPrime(Iterator, N, _WorkList) when Iterator &gt; N -&gt; thats_the_end;
findNextPrime(Iterator, N, WorkList) -&gt; I = array:get(Iterator - 1, WorkList),
 if
 I =:= empty -&gt; Iterator;
 true -&gt; findNextPrime(Iterator + 1, N, WorkList)
 end.

replace(N, L, New) -&gt; array:set(N - 1, New, L).
</code></pre>

blocks|key|1522797|text|我没有详细研究这些，但我已经测试了下面的实现(我为Project+Euler挑战编写的)，它比上面两个实现快了几个数量级。它非常慢，直到我删除了一些自定义函数，转而寻找列表:可以做同样的事情的函数。吸取教训，看看是否有你需要做的事情的库实现，这是很好的-它通常会更快！这计算了2.8+the上3.6秒内最多200万个素数的和...|type|unstyled|depth|inlineStyleRanges|entityRanges|data|1522798|%25%25%25%25%25%25%25%25%25%25%25%25%25%25%25%25%25%25%25%25%25%25%25%25%25%25%25%25%25%25%25%25%25%25%25%25%25%25%25%25%25%25%25%25%25%25%25%25%25%25%25
%25Sum+of+all+primes+below+Max.+Will+use+sieve+of+Eratosthenes+
sum_primes(Max)+->
++++LastCheck+=+round(math:sqrt(Max)),
++++All+=+lists:seq(3,+Max,+2),+%25note+are+creating+odd-only+array
++++Primes+=+sieve(All,+Max,+LastCheck),
++++%25io:format("Primes:+~p~n",+[Primes]),
++++lists:sum(Primes)+%2B+2.+%25adding+back+the+number+2+to+the+list

%25sieve+of+Eratosthenes
sieve(All,+Max,+LastCheck)+->
++++sieve([],+All,+Max,+LastCheck).

sieve(Primes,+All,+Max,+LastCheck)+->
++++%25swap+the+first+element+of+All+onto+Primes+
++++[Cur%7CAll2]+=+All,
++++Primes2+=+[Cur%7CPrimes],
++++case+Cur+>+LastCheck+of+
++++++++true+->
++++++++++++lists:append(Primes2,+All2);+%25all+known+primes+and+all+remaining+from+list+(not+sieved)+are+prime
++++++++false+->+
++++++++++++All3+=+lists:filter(fun(X)+->+X+rem+Cur+=/=+0+end,+All2),
++++++++++++sieve(Primes2,+All3,+Max,+LastCheck)

++++end.|code-block|syntax|javascript|1522799|entityMap^0|0|0^^$0|@$1|2|3|4|5|6|7|I|8|@]|9|@]|A|$]]|$1|B|3|C|5|D|7|J|8|@]|9|@]|A|$E|F]]|$1|G|3|-4|5|6|7|K|8|@]|9|@]|A|$]]]|H|$]]

I haven't studied these in detail, but I've tested my implementation below (that I wrote for a Project Euler challenge) and it's orders of magnitude faster than the above two implementations. It was excruciatingly slow until I eliminated some custom functions and instead looked for lists: functions that would do the same. It's good to learn the lesson to always see if there's a library implementation of something you need to do - it'll usually be faster! This calculates the sum of primes up to 2 million in 3.6 seconds on a 2.8GHz iMac...

<pre><code>%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%Sum of all primes below Max. Will use sieve of Eratosthenes 
sum_primes(Max) -&gt;
 LastCheck = round(math:sqrt(Max)),
 All = lists:seq(3, Max, 2), %note are creating odd-only array
 Primes = sieve(All, Max, LastCheck),
 %io:format("Primes: ~p~n", [Primes]),
 lists:sum(Primes) + 2. %adding back the number 2 to the list

%sieve of Eratosthenes
sieve(All, Max, LastCheck) -&gt;
 sieve([], All, Max, LastCheck).

sieve(Primes, All, Max, LastCheck) -&gt;
 %swap the first element of All onto Primes 
 [Cur|All2] = All,
 Primes2 = [Cur|Primes],
 case Cur &gt; LastCheck of 
 true -&gt;
 lists:append(Primes2, All2); %all known primes and all remaining from list (not sieved) are prime
 false -&gt; 
 All3 = lists:filter(fun(X) -&gt; X rem Cur =/= 0 end, All2),
 sieve(Primes2, All3, Max, LastCheck)

 end.
</code></pre>

blocks|key|1522848|text|这是我的sieve实现，它使用列表理解并尝试尾递归。我颠倒了末尾的列表，这样质数就可以排序了：|type|unstyled|depth|inlineStyleRanges|entityRanges|data|1522849|primes(Prime,+Max,+Primes,Integers)+when+Prime+>+Max+->
++++lists:reverse([Prime%7CPrimes])+%2B%2B+Integers;
primes(Prime,+Max,+Primes,+Integers)+->
++++[NewPrime%7CNewIntegers]+=+[+X+%7C%7C+X+<-+Integers,+X+rem+Prime+=/=+0+],
++++primes(NewPrime,+Max,+[Prime%7CPrimes],+NewIntegers).

primes(N)+->
++++primes(2,+round(math:sqrt(N)),+[],+lists:seq(3,N,2)).+%25+skip+odds|code-block|syntax|javascript|1522850|在我的2+2ghz上，大约需要2.8毫秒才能计算出高达2百万的素数。|1522851|entityMap^0|0|0|0^^$0|@$1|2|3|4|5|6|7|K|8|@]|9|@]|A|$]]|$1|B|3|C|5|D|7|L|8|@]|9|@]|A|$E|F]]|$1|G|3|H|5|6|7|M|8|@]|9|@]|A|$]]|$1|I|3|-4|5|6|7|N|8|@]|9|@]|A|$]]]|J|$]]

Here's my sieve implementation which uses list comprehensions and tries to be tail recursive. I reverse the list at the end so the primes are sorted:

<pre><code>primes(Prime, Max, Primes,Integers) when Prime &gt; Max -&gt;
 lists:reverse([Prime|Primes]) ++ Integers;
primes(Prime, Max, Primes, Integers) -&gt;
 [NewPrime|NewIntegers] = [ X || X &lt;- Integers, X rem Prime =/= 0 ],
 primes(NewPrime, Max, [Prime|Primes], NewIntegers).

primes(N) -&gt;
 primes(2, round(math:sqrt(N)), [], lists:seq(3,N,2)). % skip odds
</code></pre>

Takes approx 2.8 ms to calculate primes up to 2 mil on my 2ghz mac.

blocks|key|1522900|text|非常简单，精确地实现了算法，并且不使用库函数(只使用模式匹配和列表理解)。确实不是很强大。我只是试着让它尽可能的简单。|type|unstyled|depth|inlineStyleRanges|entityRanges|data|1522901|-module(primes).
-export([primes/1,+primes/2]).

primes(X)+->+sieve(range(2,+X)).
primes(X,+Y)+->+remove(primes(X),+primes(Y)).

range(X,+X)+->+[X];
range(X,+Y)+->+[X+%7C+range(X+%2B+1,+Y)].

sieve([X])+->+[X];
sieve([H+%7C+T])+->+[H+%7C+sieve(remove([H+*+X+%7C%7C+X+<-[H+%7C+T]],+T))].

remove(_,+[])+->+[];
remove([H+%7C+X],+[H+%7C+Y])+->+remove(X,+Y);
remove(X,+[H+%7C+Y])+->+[H+%7C+remove(X,+Y)].|code-block|syntax|javascript|1522902|entityMap^0|0|0^^$0|@$1|2|3|4|5|6|7|I|8|@]|9|@]|A|$]]|$1|B|3|C|5|D|7|J|8|@]|9|@]|A|$E|F]]|$1|G|3|-4|5|6|7|K|8|@]|9|@]|A|$]]]|H|$]]

Simple enough, implements exactly the algorithm, and uses no library functions (only pattern matching and list comprehension).
Not very powerful, indeed. I only tried to make it as simple as possible.

<pre><code>-module(primes).
-export([primes/1, primes/2]).

primes(X) -&gt; sieve(range(2, X)).
primes(X, Y) -&gt; remove(primes(X), primes(Y)).

range(X, X) -&gt; [X];
range(X, Y) -&gt; [X | range(X + 1, Y)].

sieve([X]) -&gt; [X];
sieve([H | T]) -&gt; [H | sieve(remove([H * X || X &lt;-[H | T]], T))].

remove(_, []) -&gt; [];
remove([H | X], [H | Y]) -&gt; remove(X, Y);
remove(X, [H | Y]) -&gt; [H | remove(X, Y)].
</code></pre>

blocks|key|1522950|text|下面是我的eratophenes实现C&C筛子：|type|unstyled|depth|inlineStyleRanges|entityRanges|data|1522951|++++-module(sieve).
++++-export([find/2,mark/2,primes/1]).

++++primes(N)+->+[2%7Clists:reverse(primes(lists:seq(2,N),2,[]))].

++++primes(_,0,[_%7CT])+->+T;
++++primes(L,P,Primes)+->+NewList+=+mark(L,P),
++++++++NewP+=+find(NewList,P),
++++++++primes(NewList,NewP,[NewP%7CPrimes]).

++++find([],_)+->+0;
++++find([H%7C_],P)+when+H+>+P+->+H;
++++find([_%7CT],P)+->+find(T,P).+


++++mark(L,P)+->+lists:reverse(mark(L,P,2,[])).

++++mark([],_,_,NewList)+->+NewList;
++++mark([_%7CT],P,Counter,NewList)+when+Counter+rem+P+=:=+0+->+mark(T,P,Counter%2B1,[P%7CNewList]);
++++mark([H%7CT],P,Counter,NewList)+->+mark(T,P,Counter%2B1,[H%7CNewList]).+|code-block|syntax|javascript|1522952|entityMap^0|0|0^^$0|@$1|2|3|4|5|6|7|I|8|@]|9|@]|A|$]]|$1|B|3|C|5|D|7|J|8|@]|9|@]|A|$E|F]]|$1|G|3|-4|5|6|7|K|8|@]|9|@]|A|$]]]|H|$]]

Here is my sieve of eratophenes implementation C&amp;C please:

<pre><code> -module(sieve).
 -export([find/2,mark/2,primes/1]).

 primes(N) -&gt; [2|lists:reverse(primes(lists:seq(2,N),2,[]))].

 primes(_,0,[_|T]) -&gt; T;
 primes(L,P,Primes) -&gt; NewList = mark(L,P),
 NewP = find(NewList,P),
 primes(NewList,NewP,[NewP|Primes]).

 find([],_) -&gt; 0;
 find([H|_],P) when H &gt; P -&gt; H;
 find([_|T],P) -&gt; find(T,P). 


 mark(L,P) -&gt; lists:reverse(mark(L,P,2,[])).

 mark([],_,_,NewList) -&gt; NewList;
 mark([_|T],P,Counter,NewList) when Counter rem P =:= 0 -&gt; mark(T,P,Counter+1,[P|NewList]);
 mark([H|T],P,Counter,NewList) -&gt; mark(T,P,Counter+1,[H|NewList]). 
</code></pre>

blocks|key|1522976|text|这是我的样品|type|unstyled|depth|inlineStyleRanges|entityRanges|data|1522977|S+=+lists:seq(2,100),
lists:foldl(fun(A,X)+->+X--[A]+end,S,[Y%7C%7CX<-S,Y<-S,X<math:sqrt(Y)%2B1,Y+rem+X==0]).|code-block|syntax|javascript|1522978|:-)|1522979|entityMap^0|0|0|0^^$0|@$1|2|3|4|5|6|7|K|8|@]|9|@]|A|$]]|$1|B|3|C|5|D|7|L|8|@]|9|@]|A|$E|F]]|$1|G|3|H|5|6|7|M|8|@]|9|@]|A|$]]|$1|I|3|-4|5|6|7|N|8|@]|9|@]|A|$]]]|J|$]]

Here is my sample

<pre><code>S = lists:seq(2,100),
lists:foldl(fun(A,X) -&gt; X--[A] end,S,[Y||X&lt;-S,Y&lt;-S,X&lt;math:sqrt(Y)+1,Y rem X==0]).
</code></pre>

:-)

I'm in the process of learning Erlang. As an exercise I picked up the <a href="http://en.wikipedia.org/wiki/Sieve_of_Eratosthenes" rel="noreferrer">Sieve of Eratosthenes</a> algorithm of generating prime numbers. Here is my code:

<pre><code>-module(seed2).
-export([get/1]).

get(N) -&gt; WorkList = lists:duplicate(N, empty),
 get(2, N, WorkList, []).

get(thats_the_end, _N, _WorkList, ResultList) -&gt; lists:reverse(ResultList);
get(CurrentPrime, N, WorkList, ResultList) -&gt; ModWorkList = markAsPrime(CurrentPrime, N, WorkList),
 NextPrime = findNextPrime(CurrentPrime + 1, N, WorkList),
 get(NextPrime, N, ModWorkList, [CurrentPrime|ResultList]).


markAsPrime(CurrentPrime, N, WorkList) when CurrentPrime =&lt; N -&gt; WorkListMod = replace(CurrentPrime, WorkList, prime),
 markAllMultiples(CurrentPrime, N, 2*CurrentPrime, WorkListMod).

markAllMultiples(_ThePrime, N, TheCurentMark, WorkList) when TheCurentMark &gt; N -&gt; WorkList;
markAllMultiples(ThePrime, N, TheCurrentMark, WorkList) -&gt; WorkListMod = replace(TheCurrentMark, WorkList, marked),
 markAllMultiples(ThePrime, N, TheCurrentMark + ThePrime, WorkListMod).

findNextPrime(Iterator, N, _WorkList) when Iterator &gt; N -&gt; thats_the_end;
findNextPrime(Iterator, N, WorkList) -&gt; I = lists:nth(Iterator, WorkList),
 if
 I =:= empty -&gt; Iterator;
 true -&gt; findNextPrime(Iterator + 1, N, WorkList)
 end.

replace(N, L, New)-&gt; {L1, [_H|L2]} = lists:split(N - 1, L),
 lists:append(L1, [New|L2]).
</code></pre>

This code actually works :) . The problem is that I have this feeling that it is not the best possible implementation. 

My question is what would be the "erlangish" way of implementing the "Sieve of Eratosthenes"

EDIT: OK, Andreas solution is very good but it is slow. Any ideas how to improve that?

Sieve of Eratosthenes in Erlang

翻译质量差，导致语言生硬或混乱。

没有提供实际的解决方法或示例。

解答不清晰，无法理解或解决问题。

页面排版不美观，阅读体验差。

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我正在学习Erlang。作为练习，我选择了生成素数的算法。下面是我的代码：-module(seed2).-export([get/1]).get(N) -> WorkList = lists:duplicate(N, empty),          get(2, N, WorkList, []).get(thats_...

问Erlang中Eratosthenes的筛子
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