Questions tagged [sieve-of-eratosthenes]

The Sieve of Eratosthenes is a prime-finding algorithm developed by the ancient Greek mathematician Eratosthenes. It works by writing down as many numbers as needed and then, traversing from lowest to highest, cross out all multiples of a number, beginning with 2. The numbers that remain are considered prime and the lowest of it will be used for the next run.

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Understanding RSA key generation and implementation in Java

Here is an attempt to leverage Java's BigInteger class to implement the RSA algorithm, as well as md5 and sha512 hashing functions to generate keys for what I hope to be strong cryptography. My prayer ...
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Zen and the Sieve of Eratosthenes - Part 1: A Basic Windowed Sieve

The Sieve of Eratosthenes is one of the oldest known algorithms and yet it is still the best method for sieving prime numbers in bulk in many situations. It is brutally simple, but to make it brutally ...
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Further Optimizing a Segmented Sieve of Eratosthenes

I've implemented a Segmented Sieve of Eratosthenes that assumes each segment is about length \$ \sqrt{N}\$ for some upper limit \$N\$. I further optimized the function by skipping all the evens when ...
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Sum of primes under a certain number

I have tried two different methods to find the sum of primes under a certain number. However both of these methods end up taking a very long time for large numbers. How can I optimise either of these ...
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Project Euler problem 50

I was just trying Project Euler problem 50. The prime 41, can be written as the sum of six consecutive primes: 41 = 2 + 3 + 5 + 7 + 11 + 13 This is the longest sum of consecutive primes that ...
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Prime Number Table, i.e. List<int>

I have written many variations of the Sieve of Eratosthenses, which is the fastest way to generate a large collection of primes. (@slepic asked for clarification, which I provide in an answer below. ...
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Eratosthenes Sieve Implementation

My friend and I were doing an Eratosthenes Sieve implementation, it works, but I think there is a mistake with "n" and with the first for condition ("i<=n"). I think that condition can cause a ...
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Sieve of Eratosthenes - segmented to increase speed and range

A lot of the sieve code floating around here and on the 'net is sloppy or broken; in fact, I've yet to see a single one that is correct, clean (in the sense of avoiding superfluous iterations etc.) ...
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Optimizing the Sieve of Eratosthenes for prime generation

I've been on a Project Euler spree and I've been solving problems and as you might know, many of them require you to use prime numbers. I've been using the following code to generate and store primes ...
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Segmented wheel Sieve of Eratosthenes in Python

Here is a new version of a segmented and wheel factorized Sieve of Eratosthenes. It currently uses mod 30 wheel factorization to eliminate multiples of 2, 3, and 5 in the sieve data structure to gain ...
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Segmented and wheel factorized prime generator in Python

I recently discovered that it is much faster to generate primes using a Sieve of Eratosthenes (SoE) with a boolean array data structure than with a heap. Since then I have been looking for fast and ...
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Wheel based unbounded sieve of Eratosthenes in Python

Answering this SO question recently, I've developed the following code (based on a well-known Active Code recipe, as discussed here): ...
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Find primes using Sieve of Eratosthenes with Python

I was Googling for a 'correct' or 'efficient' implementation of the Sieve of Eratosthenes. I found them all more complicated than what I came up with. I am by no means a Python expert, so I was ...
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Incremental Sieve of Eratosthenes Generator

So I was fiddling around with the Euler challenges. One of the things they mentioned in their discussions of the solutions is the Sieve of Eratosthenes and that you can only use it when you know an ...
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Prime Sieve and brute force

Got caught up with this morning's C++ question. So I thought I would have a go. SO here is my attempt at printing the first 1001 primes. ...
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Sum of primes up to 2 million using the Sieve of Eratosthenes

I've solved question 10 on Project Euler using the Sieve of Eratosthenes, what can I do to optimize my code? ...
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Prime sieve in Python

I was trying to write Sieve for the first time and I came up with this code: ...
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Prime Sieve and brute force #2

Based on my previous attempt. Prime Sieve and brute force Trying to make the interface simpler I have moved all the code into a class. This way I can keep track of the ...
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Find the 10001st prime number (in C++)

I wrote this solution for project Euler #7, to find the 10001th prime number using sieve of eratosthenes. It's really slow though. Any suggestions to improve performance (without using more complex ...
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Implementing Sieve of Eratosthenes faster

I wrote a version of sieve of eratosthenes: ...
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Efficiency of a recursive implementation of the Sieve of Erasthotenes in Python

I implemented the Sieve of Erasthotenes recursively using filter and I was wondering how efficient this implementation is and wether a non-recursive implementation ...
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Faster Sieve of Eratosthenes

This is an implementation of the Sieve of Eratosthenes : It takes advantages of the fact that all primes from 5 and above can be written as 6X-1 or ...
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Optimise Sieve of Eratosthenes

I have written the following code for finding out the prime numbers less than or equal to n. When I enter the input n = 10^7, my ...
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Segmented Sieve of Eratosthenes

I implemented this for the Prime Generator problem on SPOJ, but I am only getting 0.01s run-time, and would like to be able to match the run-times of the top submissions, which are all 0.00s. What ...
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Incremental Sieve of Eratosthenes using iterators

I am in the process of learning Rust and am still having some issues with borrowing and ownership. I find myself trying to borrow mutable references that are already borrowed as immutable references ...
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Incremental Sieve of Eratosthenes using unstable generators [duplicate]

I am in the process of learning Rust and am still having some issues with borrowing and ownership. I find myself trying to borrow mutable references that are already borrowed as immutable references ...
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Sieve of Eratosthenes - Python

I've been doing a lot of Project Euler lately and just wanted to make sure my implementation was as good as it could be. Does anyone have any suggestions to speed this up? ...
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Simple Sieve of Eratosthenes in Python 3

So yet another Sieve of Eratosthenes in Python 3. The function returns a list of all primes smaller but not equal max_n. The motivation is, as a practice, a ...
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Sieve of Eratosthenes: making it quicker

I was thinking about doing problem 23 of Project Euler. It includes the difficulty where you have to factorize primes. I had already done that in problems I solved earlier, but it was only necessary ...
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Find the nth prime number

It's a long time since I've written a Sieve of Eratosthenes (about 3 decades, I think, in ZX Basic). So I decided to revisit in the light of experience. Rather than allocating a vector of unknown ...
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Fast Prime Sieve (Python Implementation)

A modified version of the prime sieve. I actually doubt it could be implemented any faster, but I might be wrong: ...
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Functional Sieve of Eratosthenes in Clojure

For some reason, this is the first time I've ever written an implementation of the Sieve of Eratosthenes. I basically just stared at the Wikipedia walkthrough of the algorithm until it made sense, ...
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Computing a prime table in Rust

My objective is computing a table of primes up to n, where n is a natural number passed as an argument to the prime_table function. Here is src/lib.rs: ...
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Prime Number Generator in Swift

I would like to make (or improve my function) a function that returns an array of integers containing all the prime numbers from 2...n that can execute as quickly ...
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Short Eratosthenes Sieve

I've written a short implementation of the Eratosthenes' sieve. ...
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Improved RandomGenerator with nextPrime() method

I am trying to implement a method that generates a random prime number between a given range. I have tried using a simple method to find whether a number is prime or not, advanced simple method, ...
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Project Euler #10 (sum of primes less than two million) in Clojure

I'm new to Clojure and using some Project Euler problems to familiarize myself with the language's capabilities. Problem #10 asks to find the sum of all primes less than two million. I wanted to ...
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Sieve of Eratosthenes in Rust

This is a relatively simple implementation of the Sieve of Eratosthenes in Rust. The main objective is to find the \$n\$th prime quickly when \$n\$ might grow to huge numbers. ...
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Prime number generation - SPOJ

This is a program to generate prime numbers for a given range. The sieve of Eratosthenes algorithm was implemented, but still the SPOJ says time limit exceeded. Where can some optimizations be made? ...
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Prime number segmented sieve

I tried to solve the SPOJ prime number problem below. The code produced correct results, but Time limit exceeded and also memory need around 970M which is not efficient(?) How can I optimize this ...
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Sieve of Eratosthenes in C#

Just because I've never written a real Sieve of Eratosthenes, I decided I should probably write one just to make sure I know what it is. I'd like (constructive) criticism on best practices, potential ...
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Sieve of Eratosthenes in Python

This is yet another take in Python for the infamous Sieve of Eratosthenes. I am a beginner in Python so any criticism is highly appreciated. ...
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Get prime divisors of an Int32 using a wheel

I recently played around with prime factorization using a prime wheel. Much of the heavy lifting is done by the PrimeWheel class. I think the implementation is ...
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Custom Sieve of Eratosthenes

I'm trying to improve my code to find all the prime numbers within a set range as fast as possible, and I am trying to make it even faster. On my github page here, I have some optimization settings ...
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Finding the size of the largest connected component in a graph

Given this question, which simply can be explained as follows: Given the number of nodes and the number of edges in a graph, find the size of the largest connected component of the graph. If this ...
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“The Genuine Sieve of Eratosthenes” in C++14

The following C++ code implements the "Genuine Sieve of Eratosthenes" algorithm as described in Melissa O'Neill's classic paper. On my MacBook it computes the first 1,000,000 primes in about 11 ...
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Finding nth Prime using Python and Sieve of Eratosthenes

I'm currently working through the Project Euler Problems using HackerRank to evaluate the code and I'm stuck on the 7th Problem. ...
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Sieve of eratosthenes with std::vector<bool>

How can I improve and optimise this code? ...
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Get nth prime number using sieve of Eratosthenes

I am tasked with being able to find the \$n\$th prime number. I've tried to implement something like the sieve of Eratosthenes in increments of 200. The code works and returns the \$n\$th prime number....
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Sieve of Eratosthenes for small limits

I coded a sieve of Eratosthenes, I think it's quite fast for small limits. Any suggestions how to improve it? Especially for small limits, say limits < 50,000,000. (Also coded a parallel sieve (in ...