Last Updated : 06 Mar, 2024
Improve
Improve
Like Article
Like
Save
Report
Given a number n, print all primes smaller than or equal to n. It is also given that n is a small number.
Example:
Input : n =10
Output : 2 3 5 7Input : n = 20
Output: 2 3 5 7 11 13 17 19
The sieve of Eratosthenes is one of the most efficient ways to find all primes smaller than n when n is smaller than 10 million or so.
Recommended Problem
Techfest and the Queue
Solve Problem
Following is the algorithm to find all the prime numbers less than or equal to a given integernby the Eratosthene’s method:
When the algorithm terminates, all the numbers in the list that are not marked are prime.
Explanation with Example:
Let us take an example when n = 100. So, we need to print all prime numbers smaller than or equal to 100.
We create a list of all numbers from 2 to 100.
According to the algorithm we will mark all the numbers which are divisible by 2 and are greater than or equal to the square of it.
Now we move to our next unmarked number 3 and mark all the numbers which are multiples of 3 and are greater than or equal to the square of it.
We move to our next unmarked number 5 and mark all multiples of 5 and are greater than or equal to the square of it.
We move to our next unmarked number 7 and mark all multiples of 7 and are greater than or equal to the square of it.
We continue this process, and our final table will look like below:
So, the prime numbers are the unmarked ones: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89 and 97.
Implementation:
C++
// C++ program to print all primes smaller than or equal to
// n using Sieve of Eratosthenes
#include <bits/stdc++.h>
using namespace std;
void SieveOfEratosthenes(int n)
{
// Create a boolean array "prime[0..n]" and initialize
// all entries it as true. A value in prime[i] will
// finally be false if i is Not a prime, else true.
bool prime[n + 1];
memset(prime, true, sizeof(prime));
for (int p = 2; p * p <= n; p++) {
// If prime[p] is not changed, then it is a prime
if (prime[p] == true) {
// Update all multiples of p greater than or
// equal to the square of it numbers which are
// multiple of p and are less than p^2 are
// already been marked.
for (int i = p * p; i <= n; i += p)
prime[i] = false;
}
}
// Print all prime numbers
for (int p = 2; p <= n; p++)
if (prime[p])
cout << p << " ";
}
// Driver Code
int main()
{
int n = 30;
cout << "Following are the prime numbers smaller "
<< " than or equal to " << n << endl;
SieveOfEratosthenes(n);
return 0;
}
C
// C program to print all primes smaller than or equal to
// n using Sieve of Eratosthenes
#include <stdio.h>
#include <stdbool.h>
#include <string.h>
void SieveOfEratosthenes(int n)
{
// Create a boolean array "prime[0..n]" and initialize
// all entries it as true. A value in prime[i] will
// finally be false if i is Not a prime, else true.
bool prime[n + 1];
memset(prime, true, sizeof(prime));
for (int p = 2; p * p <= n; p++) {
// If prime[p] is not changed, then it is a prime
if (prime[p] == true) {
// Update all multiples of p greater than or
// equal to the square of it numbers which are
// multiple of p and are less than p^2 are
// already been marked.
for (int i = p * p; i <= n; i += p)
prime[i] = false;
}
}
// Print all prime numbers
for (int p = 2; p <= n; p++)
if (prime[p])
printf("%d ",p);
}
// Driver Code
int main()
{
int n = 30;
printf("Following are the prime numbers smaller than or equal to %d \n", n);
SieveOfEratosthenes(n);
return 0;
}
// This code is contributed by Aditya Kumar (adityakumar129)
Java
// Java program to print all primes smaller than or equal to
// n using Sieve of Eratosthenes
class SieveOfEratosthenes {
void sieveOfEratosthenes(int n)
{
// Create a boolean array "prime[0..n]" and
// initialize all entries it as true. A value in
// prime[i] will finally be false if i is Not a
// prime, else true.
boolean prime[] = new boolean[n + 1];
for (int i = 0; i <= n; i++)
prime[i] = true;
for (int p = 2; p * p <= n; p++) {
// If prime[p] is not changed, then it is a
// prime
if (prime[p] == true) {
// Update all multiples of p greater than or
// equal to the square of it numbers which
// are multiple of p and are less than p^2
// are already been marked.
for (int i = p * p; i <= n; i += p)
prime[i] = false;
}
}
// Print all prime numbers
for (int i = 2; i <= n; i++) {
if (prime[i] == true)
System.out.print(i + " ");
}
}
// Driver Code
public static void main(String args[])
{
int n = 30;
System.out.print("Following are the prime numbers ");
System.out.println("smaller than or equal to " + n);
SieveOfEratosthenes g = new SieveOfEratosthenes();
g.sieveOfEratosthenes(n);
}
}
// This code is contributed by Aditya Kumar (adityakumar129)
C#
// C# program to print all primes
// smaller than or equal to n
// using Sieve of Eratosthenes
using System;
namespace prime {
public class GFG {
public static void SieveOfEratosthenes(int n)
{
// Create a boolean array
// "prime[0..n]" and
// initialize all entries
// it as true. A value in
// prime[i] will finally be
// false if i is Not a
// prime, else true.
bool[] prime = new bool[n + 1];
for (int i = 0; i <= n; i++)
prime[i] = true;
for (int p = 2; p * p <= n; p++)
{
// If prime[p] is not changed,
// then it is a prime
if (prime[p] == true)
{
// Update all multiples of p
for (int i = p * p; i <= n; i += p)
prime[i] = false;
}
}
// Print all prime numbers
for (int i = 2; i <= n; i++)
{
if (prime[i] == true)
Console.Write(i + " ");
}
}
// Driver Code
public static void Main()
{
int n = 30;
Console.WriteLine(
"Following are the prime numbers");
Console.WriteLine("smaller than or equal to " + n);
SieveOfEratosthenes(n);
}
}
}
// This code is contributed by Sam007.
Javascript
<script>
// javascript program to print all
// primes smaller than or equal to
// n using Sieve of Eratosthenes
function sieveOfEratosthenes(n)
{
// Create a boolean array
// "prime[0..n]" and
// initialize all entries
// it as true. A value in
// prime[i] will finally be
// false if i is Not a
// prime, else true.
prime = Array.from({length: n+1}, (_, i) => true);
for (p = 2; p * p <= n; p++)
{
// If prime[p] is not changed, then it is a
// prime
if (prime[p] == true)
{
// Update all multiples of p
for (i = p * p; i <= n; i += p)
prime[i] = false;
}
}
// Print all prime numbers
for (i = 2; i <= n; i++)
{
if (prime[i] == true)
document.write(i + " ");
}
}
// Driver Code
var n = 30;
document.write(
"Following are the prime numbers ");
document.write("smaller than or equal to " + n+"<br>");
sieveOfEratosthenes(n);
// This code is contributed by 29AjayKumar
</script>
PHP
<?php
// php program to print all primes smaller
// than or equal to n using Sieve of
// Eratosthenes
function SieveOfEratosthenes($n)
{
// Create a boolean array "prime[0..n]"
// and initialize all entries it as true.
// A value in prime[i] will finally be
// false if i is Not a prime, else true.
$prime = array_fill(0, $n+1, true);
for ($p = 2; $p*$p <= $n; $p++)
{
// If prime[p] is not changed,
// then it is a prime
if ($prime[$p] == true)
{
// Update all multiples of p
for ($i = $p*$p; $i <= $n; $i += $p)
$prime[$i] = false;
}
}
// Print all prime numbers
for ($p = 2; $p <= $n; $p++)
if ($prime[$p])
echo $p." ";
}
// Driver Code
$n = 30;
echo "Following are the prime numbers "
."smaller than or equal to " .$n."\n" ;
SieveOfEratosthenes($n);
// This code is contributed by mits
?>
Python3
# Python program to print all
# primes smaller than or equal to
# n using Sieve of Eratosthenes
def SieveOfEratosthenes(n):
# Create a boolean array
# "prime[0..n]" and initialize
# all entries it as true.
# A value in prime[i] will
# finally be false if i is
# Not a prime, else true.
prime = [True for i in range(n+1)]
p = 2
while (p * p <= n):
# If prime[p] is not
# changed, then it is a prime
if (prime[p] == True):
# Update all multiples of p
for i in range(p * p, n+1, p):
prime[i] = False
p += 1
# Print all prime numbers
for p in range(2, n+1):
if prime[p]:
print(p)
# Driver code
if __name__ == '__main__':
n = 20
print("Following are the prime numbers smaller"),
print("than or equal to", n)
SieveOfEratosthenes(n)
Output
Following are the prime numbers smaller than or equal to 302 3 5 7 11 13 17 19 23 29
Time Complexity: O(N*log(log(N)))
Auxiliary Space: O(N)
You may also like to see:
- How is the time complexity of Sieve of Eratosthenes is n*log(log(n))?
- Segmented Sieve.
- Sieve of Eratosthenes in O(n) time complexity
${secondsToHms(duration)}
${getTagsString(tags)}
'; } else{ let view_all_url = `${GFG_SITE_URL}videos/`; videos_content+=`
View All
`; } // videos_content+= '
'; } } return videos_content; } //function to show main video content with related videos content async function showMainVideoContent(main_video, course_link){ //Load main video $(".video-main").html(`
`); require(["ima"], function() { var player = videojs('article-video', { controls: true, // autoplay: true, // muted: true, controlBar: { pictureInPictureToggle: false }, playbackRates: [0.5, 0.75, 1, 1.25, 1.5, 2], poster: main_video['meta']['largeThumbnail'], sources: [{src: main_video['source'], type: 'application/x-mpegURL'}], tracks: [{src: main_video['subtitle'], kind:'captions', srclang: 'en', label: 'English', default: true}] },function() { player.qualityLevels(); try { player.hlsQualitySelector(); } catch (error) { console.log("HLS not working - ") } } ); const video = document.querySelector("video"); const events =[ { 'name':'play', 'callback':()=>{videoPlayCallback(main_video['slug'])} }, ]; events.forEach(event=>{ video.addEventListener(event.name,event.callback); }); }, function (err) { var player = videojs('article-video'); player.createModal('Something went wrong. Please refresh the page to load the video.'); }); /*let video_date = main_video['time']; video_date = video_date.split("/"); video_date = formatDate(video_date[2], video_date[1], video_date[0]); let share_section_content = `
${video_date}
`;*/ let hasLikeBtn = false; // console.log(share_section_content); var data = {}; if(false){ try { if((loginData && loginData.isLoggedIn == true)){ const resp = await fetch(`${API_SCRIPT_URL}logged-in-video-details/${main_video['slug']}/`,{ credentials: 'include' }) if(resp.status == 200 || resp.status == 201){ data = await resp.json(); share_section_content+= `
`; hasLikeBtn = true; } else { share_section_content+= `
`; } } else { share_section_content+= `
`; } //Load share section // $(".video-share-section").html(share_section_content); // let exitCond = 0; // const delay = (delayInms) => { // return new Promise(resolve => setTimeout(resolve, delayInms)); // } // while(!loginData){ // let delayres = await delay(1000); // exitCond+=1; // console.log(exitCond); // if(exitCond>5){ // break; // } // } // console.log(loginData); /*if(hasLikeBtn && loginData && loginData.isLoggedIn == true){ setLiked(data.liked) setSaved(data.watchlist) }*/ } catch (error) { console.log(error); } } //Load video content like title, description if(false){ $(".video-content-section").html(`
${main_video['title']}
${hideMainVideoDescription(main_video['description'], main_video['id'])}
${getTagsString(main_video['category'])} ${(course_link.length)? `
View Course
`:''} `); let related_vidoes = main_video['recommendations']; if(!!videos && videos.length>0){ //Load related videos $(".related-videos-content").html(getvideosContent()); } } //show video content element = document.getElementById('article-video-tab-content'); element.style.display = 'block'; $('.spinner-loading-overlay:eq(0)').remove(); $('.spinner-loading-overlay:eq(0)').remove(); } await showMainVideoContent(video_data, course_link); // fitRelatedVideosDescription(); } catch (error) { console.log(error); } } getVideoData(); /* $(window).resize(function(){ onWidthChangeEventsListener(); }); $('#video_nav_tab').click('on', function(){ fitRelatedVideosDescription(); });*/ });
