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• Can anyone explain segmented sieve of eratosthenes [on hold]

  - by Utkarsh

  I've searched all over the web on implementation of segmented sieve of eratosthenes. But I found none of them suitable for a beginner. Can anyone explain me the underlying principle behind this method? EDIT: I know that in Sieve of Eratosthenes, we find all primes upto the square root of given number and cross out all multiples of them till the given number. But what do we exactly do in its segmented version?

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• Time complexity of Sieve of Eratosthenes algorithm

  - by eSKay

  From Wikipedia: The complexity of the algorithm is O(n(logn)(loglogn)) bit operations. How do you arrive at that? That the complexity includes the loglogn term tells me that there is a sqrt(n) somewhere. Suppose I am running the sieve on the first 100 numbers (n = 100), assuming that marking the numbers as composite takes constant time (array implementation), the number of times we use mark_composite() would be something like n/2 + n/3 + n/5 + n/7 + ... + n/97 = O(n) And to find the next prime number (for example to jump to 7 after crossing out all the numbers that are multiples of 5), the number of operations would be O(n). So, the complexity would be O(n^2). Do you agree?

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• Clojure - tail recursive sieve of Eratosthenes

  - by Konrad Garus

  I have this implementation of the sieve of Eratosthenes in Clojure: (defn sieve [n] (loop [last-tried 2 sift (range 2 (inc n))] (if (or (nil? last-tried) (> last-tried n)) sift (let [filtered (filter #(or (= % last-tried) (< 0 (rem % last-tried))) sift)] (let [next-to-try (first (filter #(> % last-tried) filtered))] (recur next-to-try filtered)))))) For larger n (like 20000) it ends with stack overflow. Why doesn't tail call elimination work here? How to fix it?

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• The sieve of Eratosthenes in F#

  - by IVlad

  I am interested in an implementation of the sieve of eratosthenes in purely functional F#. I am interested in an implementation of the actual sieve, not the naive functional implementation that isn't really the sieve, so not something like this: let rec PseudoSieve list = match list with | hd::tl -> hd :: (PseudoSieve <| List.filter (fun x -> x % hd <> 0) tl) | [] -> [] The second link above briefly describes an algorithm that would require the use of a multimap, which isn't available in F# as far as I know. The Haskell implementation given uses a map that supports an insertWith method, which I haven't seen available in the F# functional map. Does anyone know a way to translate the given Haskell map code to F#, or perhaps knows of alternative implementation methods or sieving algorithms that are as efficient and better suited for a functional implementation or F#?

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• Speed up bitstring/bit operations in Python?

  - by Xavier Ho

  I wrote a prime number generator using Sieve of Eratosthenes and Python 3.1. The code runs correctly and gracefully at 0.32 seconds on ideone.com to generate prime numbers up to 1,000,000. # from bitstring import BitString def prime_numbers(limit=1000000): '''Prime number generator. Yields the series 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 ... using Sieve of Eratosthenes. ''' yield 2 sub_limit = int(limit**0.5) flags = [False, False] + [True] * (limit - 2) # flags = BitString(limit) # Step through all the odd numbers for i in range(3, limit, 2): if flags[i] is False: # if flags[i] is True: continue yield i # Exclude further multiples of the current prime number if i <= sub_limit: for j in range(i*3, limit, i<<1): flags[j] = False # flags[j] = True The problem is, I run out of memory when I try to generate numbers up to 1,000,000,000. flags = [False, False] + [True] * (limit - 2) MemoryError As you can imagine, allocating 1 billion boolean values (1 byte 4 or 8 bytes (see comment) each in Python) is really not feasible, so I looked into bitstring. I figured, using 1 bit for each flag would be much more memory-efficient. However, the program's performance dropped drastically - 24 seconds runtime, for prime number up to 1,000,000. This is probably due to the internal implementation of bitstring. You can comment/uncomment the three lines to see what I changed to use BitString, as the code snippet above. My question is, is there a way to speed up my program, with or without bitstring?

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• Clojure: Avoiding stack overflow in Sieve of Erathosthene?

  - by nixx

  Here's my implementation of Sieve of Erathosthene in Clojure (based on SICP lesson on streams): (defn nats-from [n] (iterate inc n)) (defn divide? [p q] (zero? (rem q p))) (defn sieve [stream] (lazy-seq (cons (first stream) (sieve (remove #(divide? (first stream) %) (rest stream)))))) (def primes (sieve (nats-from 2))) Now, it's all OK when i take first 100 primes: (take 100 primes) But, if i try to take first 1000 primes, program breaks because of stack overflow. I'm wondering if is it possible to change somehow function sieve to become tail-recursive and, still, to preserve "streamnes" of algorithm? Any help???

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• Actionscript - Dropping Multiple Objects Using an Array?

  - by Eratosthenes

  I'm trying to get these fireBalls to drop more often, im not sure if im using Math.random correctly also, for some reason I'm getting a null reference because I think the fireBalls array waits for one to leave the stage before dropping another one? this is the relevant code: var sun:Sun=new Sun var fireBalls:Array=new Array() var left:Boolean; function onEnterFrame(event:Event){ if (left) { sun.x = sun.x - 15; }else{ sun.x = sun.x + 15; } if (fireBalls.length>0&&fireBalls[0].y>stage.stageHeight){ // Fireballs exit stage removeChild(fireBalls[0]); fireBalls.shift(); } for (var j:int=0; j<fireBalls.length; j++){ fireBalls[j].y=fireBalls[j].y+15; if (fireBalls[j].y>stage.stageHeight-fireBall.width/2){ } } if (Math.random()<.2){ // Fireballs shooting from Sun var fireBall:FireBall=new FireBall; fireBall.x=sun.x; addChild(fireBall); fireBalls.push(fireBall); } }

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• Dropping multiple objects using an array in Actionscript?

  - by Eratosthenes

  I'm trying to get these fireBalls to drop more often, I'm not sure if I'm using Math.random correctly. Also, for some reason I'm getting a null reference because I think the fireBalls array waits for one to leave the stage before dropping another one? This is the relevant code: var sun:Sun=new Sun var fireBalls:Array=new Array() var left:Boolean; function onEnterFrame(event:Event){ if (left) { sun.x = sun.x - 15; }else{ sun.x = sun.x + 15; } if (fireBalls.length>0&&fireBalls[0].y>stage.stageHeight){ // Fireballs exit stage removeChild(fireBalls[0]); fireBalls.shift(); } for (var j:int=0; j<fireBalls.length; j++){ fireBalls[j].y=fireBalls[j].y+15; if (fireBalls[j].y>stage.stageHeight-fireBall.width/2){ } } if (Math.random()<.2){ // Fireballs shooting from Sun var fireBall:FireBall=new FireBall; fireBall.x=sun.x; addChild(fireBall); fireBalls.push(fireBall); } }

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• Actionscript - Dropping Multiple Objects Using an Array? [closed]

  - by Eratosthenes

  Possible Duplicate: Actionscript - Dropping Multiple Objects Using an Array? I'm trying to get these fireBalls to drop more often, im not sure if im using Math.random correctly also, for some reason I'm getting a null reference because I think the fireBalls array waits for one to leave the stage before dropping another one? this is the relevant code: var sun:Sun=new Sun var fireBalls:Array=new Array() var left:Boolean; function onEnterFrame(event:Event){ if (left) { sun.x = sun.x - 15; }else{ sun.x = sun.x + 15; } if (fireBalls.length>0&&fireBalls[0].y>stage.stageHeight){ // Fireballs exit stage removeChild(fireBalls[0]); fireBalls.shift(); } for (var j:int=0; j<fireBalls.length; j++){ fireBalls[j].y=fireBalls[j].y+15; if (fireBalls[j].y>stage.stageHeight-fireBall.width/2){ } } if (Math.random()<.2){ // Fireballs shooting from Sun var fireBall:FireBall=new FireBall; fireBall.x=sun.x; addChild(fireBall); fireBalls.push(fireBall); } }

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• Express any number as the sum of 4 prime numbers [Doubts]

  - by WarDoGG

  I was give a problem to express any number as sum of 4 prime numbers. Conditions: Not allowed to use any kind of database. Maximum execution time : 3 seconds Numbers only till 100,000 If the splitting is NOT possible, then return -1 What i did : using the sieve of eratosthenes, i calculated all prime numbers till the specified number. looked up a concept called goldbach conjecture which expresses an even number as the summation of 2 primes. However, i am stuck beyond that. Can anyone help me on this one as to what approach u might take ? The sieve of eratosthenes is taking 2 seconds to count primes till 100,000 :(((

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• Finding a prime number after a given number

  - by avd

  How can I find the least prime number greater than a given number? For example, given 4, I need 5; given 7, I need 11. I would like to know some ideas on best algorithms to do this. One method that I thought of was generate primes numbers through the Sieve of Eratosthenes, and then find the prime after the given number.

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• Chain call in clojure?

  - by Konrad Garus

  I'm trying to implement sieve of Eratosthenes in Clojure. One approach I would like to test is this: Get range (2 3 4 5 6 ... N) For 2 <= i <= N Pass my range through filter that removes multiplies of i For i+1th iteration, use result of the previous filtering I know I could do it with loop/recur, but this is causing stack overflow errors (for some reason tail call optimization is not applied). How can I do it iteratively? I mean invoking N calls to the same routine, passing result of ith iteration to i+1th.

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• nth ugly number

  - by Anil Katti

  Numbers whose only prime factors are 2, 3 or 5 are called ugly numbers. Example: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, ... 1 can be considered as 2^0. I am working on finding nth ugly number. Note that these numbers are extremely sparsely distributed as n gets large. I wrote a trivial program that computes if a given number is ugly or not. For n 500 - it became super slow. I tried using memoization - observation: ugly_number * 2, ugly_number * 3, ugly_number * 5 are all ugly. Even with that it is slow. I tried using some properties of log - since that will reduce this problem from multiplication to addition - but, not much luck yet. Thought of sharing this with you all. Any interesting ideas? Using a concept similar to "Sieve of Eratosthenes" (thanks Anon) for (int i(2), uglyCount(0); ; i++) { if (i % 2 == 0) continue; if (i % 3 == 0) continue; if (i % 5 == 0) continue; uglyCount++; if (uglyCount == n - 1) break; } i is the nth ugly number. Even this is pretty slow. I am trying to find 1500th ugly number.

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• Recursively adding threads to a Java thread pool

  - by Leith

  I am working on a tutorial for my Java concurrency course. The objective is to use thread pools to compute prime numbers in parallel. The design is based on the Sieve of Eratosthenes. It has an array of n bools, where n is the largest integer you are checking, and each element in the array represents one integer. True is prime, false is non prime, and the array is initially all true. A thread pool is used with a fixed number of threads (we are supposed to experiment with the number of threads in the pool and observe the performance). A thread is given a integer multiple to process. The thread then finds the first true element in the array that is not a multiple of thread's integer. The thread then creates a new thread on the thread pool which is given the found number. After a new thread is formed, the existing thread then continues to set all multiples of it's integer in the array to false. The main program thread starts the first thread with the integer '2', and then waits for all spawned threads to finish. It then spits out the prime numbers and the time taken to compute. The issue I have is that the more threads there are in the thread pool, the slower it takes with 1 thread being the fastest. It should be getting faster not slower! All the stuff on the internet about Java thread pools create n worker threads the main thread then wait for all threads to finish. The method I use is recursive as a worker can spawn more worker threads. I would like to know what is going wrong, and if Java thread pools can be used recursively.

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• ruby comma operator and step question

  - by ryan_m

  so, i'm trying to learn ruby by doing some project euler questions, and i've run into a couple things i can't explain, and the comma ?operator? is in the middle of both. i haven't been able to find good documentation for this, maybe i'm just not using the google as I should, but good ruby documentation seems a little sparse . . . 1: how do you describe how this is working? the first snippet is the ruby code i don't understand, the second is the code i wrote that does the same thing only after painstakingly tracing the first: #what is this doing? cur, nxt = nxt, cur + nxt #this, apparently, but how to describe the above? nxt = cur + nxt cur = nxt - cur 2: in the following example, how do you describe what the line with 'step' is doing? from what i can gather, the step command works like (range).step(step_size), but this seems to be doing (starting_point).step(ending_point, step_size). Am i right with this assumption? where do i find good doc of this? #/usr/share/doc/ruby1.9.1-examples/examples/sieve.rb # sieve of Eratosthenes max = Integer(ARGV.shift || 100) sieve = [] for i in 2 .. max sieve[i] = i end for i in 2 .. Math.sqrt(max) next unless sieve[i] (i*i).step(max, i) do |j| sieve[j] = nil end end puts sieve.compact.join(", ")

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• "EXC_BAD_ACCESS: Unable to restore previously selected frame" Error, Array size?

  - by Job

  Hi there, I have an algorithm for creating the sieve of Eratosthenes and pulling primes from it. It lets you enter a max value for the sieve and the algorithm gives you the primes below that value and stores these in a c-style array. Problem: Everything works fine with values up to 500.000, however when I enter a large value -while running- it gives me the following error message in xcode: Program received signal: “EXC_BAD_ACCESS”. warning: Unable to restore previously selected frame. Data Formatters temporarily unavailable, will re-try after a 'continue'. (Not safe to call dlopen at this time.) My first idea was that I didn't use large enough variables, but as I am using 'unsigned long long int', this should not be the problem. Also the debugger points me to a point in my code where a point in the array get assigned a value. Therefore I wonder is there a maximum limit to an array? If yes: should I use NSArray instead? If no, then what is causing this error based on this information? EDIT: This is what the code looks like (it's not complete, for it fails at the last line posted). I'm using garbage collection. /*--------------------------SET UP--------------------------*/ unsigned long long int upperLimit = 550000; // unsigned long long int sieve[upperLimit]; unsigned long long int primes[upperLimit]; unsigned long long int indexCEX; unsigned long long int primesCounter = 0; // Fill sieve with 2 to upperLimit for(unsigned long long int indexA = 0; indexA < upperLimit-1; ++indexA) { sieve[indexA] = indexA+2; } unsigned long long int prime = 2; /*-------------------------CHECK & FIND----------------------------*/ while(!((prime*prime) > upperLimit)) { //check off all multiples of prime for(unsigned long long int indexB = prime-2; indexB < upperLimit-1; ++indexB) { // Multiple of prime = 0 if(sieve[indexB] != 0) { if(sieve[indexB] % prime == 0) { sieve[indexB] = 0; } } } /*---------------- Search for next prime ---------------*/ // index of current prime + 1 unsigned long long int indexC = prime - 1; while(sieve[indexC] == 0) { ++indexC; } prime = sieve[indexC]; // Store prime in primes[] primes[primesCounter] = prime; // This is where the code fails if upperLimit > 500000 ++primesCounter; indexCEX = indexC + 1; } As you may or may not see, is that I am -very much- a beginner. Any other suggestions are welcome of course :)

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• CodePlex Daily Summary for Tuesday, March 08, 2011

  CodePlex Daily Summary for Tuesday, March 08, 2011Popular ReleasesAjax Minifier: AjaxMin 4.14: Fixed issue with CSS3 @media and @page parsing. Added support for more properties in the MSBuild task.DotNetAge -a lightweight Mvc jQuery CMS: DotNetAge 2: What is new in DotNetAge 2.0 ? Completely update DJME to DJME2, enhance user experience ,more beautiful and more interactively visit DJME project home to lean more about DJME http://www.dotnetage.com/sites/home/djme.html A new widget engine has came! Faster and easiler. Runtime performance enhanced. SEO enhanced. UI Designer enhanced. A new web resources explorer. Page manager enhanced. BlogML supports added that allows you import/export your blog data to/from dotnetage publishi...Master Data Services Manager: stable 1.0.3: Update 2011-03-07 : bug fixes added external configuration File : configuration.config added TreeView Display of model (still in dev) http://img96.imageshack.us/img96/5067/screenshot073l.jpg added Connection Parameters (username, domain, password, stored encrypted in configuration file) http://img402.imageshack.us/img402/5350/screenshot072qc.jpgSharePoint Content Inventory: Release 1.1: Release 1.1Menu and Context Menu for Silverlight 4.0: Silverlight Menu and Context Menu v2.4 Beta: - Moved the core of the PopupMenu class to the new PopupMenuBase class. - Renamed the MenuTriggerElement class to MenuTriggerRelationship. - Renamed the ApplicationMenus property to MenuTriggers. - Renamed the _allowPinnedState property to AllowPinnedState. - Renamed the _restoreFocusOnClose property to RestoreFocusOnClose. - Renamed the SubmenuLaunchKey property to FlyoutKey. - Renamed the AutoMapTriggerElementToSelectableItem property to UseSelectedItemAsTriggerElement. - Renamed the AutoM...Kooboo CMS: Kooboo CMS 3.0 Beta: Files in this downloadkooboo_CMS.zip: The kooboo application files Content_DBProvider.zip: Additional content database implementation of MSSQL,SQLCE, RavenDB and MongoDB. 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The binaries are also available via NuGet: AspNetSprites-Core AspNetSprites-WebFormsControl AspNetSprites-MvcAndRazorHelper It includes the foll...New ProjectsCaxangáV2: Ainda jogando Caxangá.. ou nãoCollection Membership Wizard for SCCM: This application assists SMS 2003 and SCCM 2007 administrators with the everyday task of adding lists of computers or users by name to collections in their hierarchy. The goal of this application is to be very easy to use and to have good performance.CoseaDirectos: Aplicación asp.net, silverlight, sql server 2008 para reclutamiento de personal DoctrineIgniter: Usage of Doctrine 2 ORM and Codeigniter 2 PHP platform.Field Finder: DB Administration tool. Easy search in the SQL server database structure. Provides predefined templates for SQL Scripts and VB.NET source code. Search in database Structure and database Data. 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It's developed in C#, and interfaces with various web services, including imdb, and thetvdbLaptop Rental System: This project is for Laptop Rental Software project. It will lasts for 2 weeks. Xuan ChienMathLib.NET: Aims to provide a fully managed implementation of core MATLAB(R) functions, designed to be used from dynamic languages such as IronPython and providing an API matching the MATLAB(R) API, to ease the transition from analysis to implementation.Mobile Application Development Framework: A general purpose Windows CE/Mobile Application Development FrameworkMSMSpec: MSMSpec autogenerates MSTest tests corresponding to MSpec tests. Useful where MSTest integration is desired / required / forced. Also enables using VS test tooling for MSpec tests. Requires VS2010 and .NET 4.0.Multi-touch GIS API for TableTops: This API facilitates the creation of multi-touch GIS applications for digital Tabletops. It is built on top of ESRI API for WPF 4.0 and it uses Windows 7 touch events. It also uses some gestures from the Gesture Toolkit.NewLineReplacer: Replace letter fast and easy in great textfilesOpenGLMaciejLis: Project is a game prototype created in C++ and OpenGLPlanetQuest: Application to poll the current extra-solar planet count at http://planetquest.jpl.nasa.gov/ Prime number exporter: Prime number exporter calculates prime numbers using the "Sieve of Eratosthenes" and exports a Textfile. QPAPrintLib: Print every document by its recommended programmRegistry Editor for Windows Mobile: A registry editor for Windows Mobile 6.x and 5.x based devices.Remote desktop on mobile phones: Mobile Remote Desktop enables you to connect to your computer from your mobile devices using bluetooth connectivity. Once connected, Mobile Remote Desktop gives you mouse and keyboard control of your computer from mobile.RestUpProxy: RestUpProxy is a .Net REST client designed to make using RESTful APIs a snap.SharePoint 2010 List Based 404 Handler: A SharePoint WSP that customises the 404 handler for a web application, allowing you to define how to handle missing page requests via a SharePoint list. This is the SharePoint 2010 version.SharePoint Content Inventory: SPContentInventory generates a complete content invetory for SharePoint 2007/2010 sites. The content inventory is exported as an Excel file providing information about all sites, lists and libraries.Shop: open source ecommerce solution for umbraco.SilverVision: Computer vision algorithms implementation in SilverlightSpCop: The aim of this project is to offer a utility similar to fxcop but for wsp packages. At the end it should contain enough rules to ensure good practices and allow automated audits or checks at build time for example.Syscable: Sistema para control de mensualidades para una empresa que proporcione servicios de television por cableSyscart: Aplicacion web para manejo de inventario en bodegas u otros establecimientos. Tranquility.Net (Wcf App Server): Allows developers to host multiple isolated Wcf services within a single Windows service. You'll no longer have to use IIS to host all your services. It's developed in C# .NET. Your services with a smile.USMC Knowledge for WP7: USMC Knowledge is an information application to provide active duty Marines, as well as those with an interest in the USMC with basic knowledge. It's developed in Silverlight for Windows Phone 7.Utility4Net: some base class such as xml,string,data,secerity,web,office... etc.. under Microsoft.NET Framework 4.0 by c# Part of the code r collected from the Internet WPF ImageUitls: WPF Image Utils is a set of image related applications that use WPF. Currently the project focuses on a picture viewerZen4Sync, Orchestration and Test Load platform for SQL Server Merge Replication: This project is all about providing a orchestration and test load platform able to validate any SQL Server Merge Replication based Architecture.Zimms: Collaboration Site for friends, a code depot, and scratch pad??tbl??????: ????tbl?????????。 ??tbl??????，??????????，?????、excel???。 ?????????????，????，????????！

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• Simple prime number program - Weird issue with threads C#

  - by Para

  Hi! This is my code: using System; using System.Collections.Generic; using System.Linq; using System.Text; using System.Threading; namespace FirePrime { class Program { static bool[] ThreadsFinished; static bool[] nums; static bool AllThreadsFinished() { bool allThreadsFinished = false; foreach (var threadFinished in ThreadsFinished) { allThreadsFinished &= threadFinished; } return allThreadsFinished; } static bool isPrime(int n) { if (n < 2) { return false; } if (n == 2) { return true; } if (n % 2 == 0) { return false; } int d = 3; while (d * d <= n) { if (n % d == 0) { return false; } d += 2; } return true; } static void MarkPrimes(int startNumber,int stopNumber,int ThreadNr) { for (int j = startNumber; j < stopNumber; j++) nums[j] = isPrime(j); lock (typeof(Program)) { ThreadsFinished[ThreadNr] = true; } } static void Main(string[] args) { int nrNums = 100; int nrThreads = 10; //var threadStartNums = new List<int>(); ThreadsFinished = new bool[nrThreads]; nums = new bool[nrNums]; //var nums = new List<bool>(); nums[0] = false; nums[1] = false; for(int i=2;i<nrNums;i++) nums[i] = true; int interval = (int)(nrNums / nrThreads); //threadStartNums.Add(2); //int aux = firstStartNum; //int i = 2; //while (aux < interval) //{ // aux = interval*i; // i=i+1; // threadStartNums.Add(aux); //} int startNum = 0; for (int i = 0; i < nrThreads; i++) { var _thread = new System.Threading.Thread(() => MarkPrimes(startNum, Math.Min(startNum + interval, nrNums), i)); startNum = startNum + interval; //set the thread to run in the background _thread.IsBackground = true; //start our thread _thread.Start(); } while (!AllThreadsFinished()) { Thread.Sleep(1); } for (int i = 0; i < nrNums; i++) if(nums[i]) Console.WriteLine(i); } } } This should be a pretty simple program that is supposed to find and output the first nrNums prime numbers using nrThreads threads working in parallel. So, I just split nrNums into nrThreads equal chunks (well, the last one won't be equal; if nrThreads doesn't divide by nrNums, it will also contain the remainder, of course). I start nrThreads threads. They all test each number in their respective chunk and see if it is prime or not; they mark everything out in a bool array that keeps a tab on all the primes. The threads all turn a specific element in another boolean array ThreadsFinished to true when they finish. Now the weird part begins: The threads never all end. If I debug, I find that ThreadNr is not what I assign to it in the loop but another value. I guess this is normal since the threads execute afterwards and the counter (the variable i) is already increased by then but I cannot understand how to make the code be right. Can anyone help? Thank you in advance. P.S.: I know the algorithm is not very efficient; I am aiming at a solution using the sieve of Eratosthenes also with x given threads. But for now I can't even get this one to work and I haven't found any examples of any implementations of that algorithm anywhere in a language that I can understand.

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