DEV Community

Cover image for Sieve of Eratosthenes
Deepak Raj
Deepak Raj

Posted on • Edited on

9 5

Sieve of Eratosthenes

Sieve of Eratosthenes

Topic: Sieve of Eratosthenes

In mathematics, the sieve of Eratosthenes is an ancient algorithm for finding all prime numbers up to any given limit. It does so by iteratively marking as composite the multiples of each prime, starting with the first prime number, 2.

Example:-

Input : n = 10
Output : 2 3 5 7 

Input : n = 20 
Output: 2 3 5 7 11 13 17 19
Enter fullscreen mode Exit fullscreen mode

Steps to Implement sieve of Eratosthenes

  • Create a list of consecutive integers from 2 to n: (2, 3, 4, …, n).

  • Initially, let p equal 2, the first prime number.

  • Starting from p2, count up in increments of p and mark each of these numbers greater than or equal to p2 itself in the list. These numbers will be p(p+1), p(p+2), p(p+3), etc..

  • Find the first number greater than p in the list that is not marked. If there was no such number, stop. Otherwise, let p now equal this number (which is the next prime), and repeat from step 3.

Implementation of Sieve of Eratosthenes in Python3.

def get_primes(n):
  m = n+1
  #numbers = [True for i in range(m)]
  numbers = [True] * m #EDIT: faster
  for i in range(2, int(n**0.5 + 1)):
    if numbers[i]:
      for j in range(i*i, m, i):
        numbers[j] = False
  primes = []
  for i in range(2, m):
    if numbers[i]:
      primes.append(i)
  return primes

print(get_primes(25))
Enter fullscreen mode Exit fullscreen mode

Image of Timescale

🚀 pgai Vectorizer: SQLAlchemy and LiteLLM Make Vector Search Simple

We built pgai Vectorizer to simplify embedding management for AI applications—without needing a separate database or complex infrastructure. Since launch, developers have created over 3,000 vectorizers on Timescale Cloud, with many more self-hosted.

Read more

Top comments (1)

Collapse
 
muhimen123 profile image
Muhimen

Cool, you are going advanced! Keep it up.

Postmark Image

Speedy emails, satisfied customers

Are delayed transactional emails costing you user satisfaction? Postmark delivers your emails almost instantly, keeping your customers happy and connected.

Sign up