Breaking News: Grepper is joining You.com. Read the official announcement!

How to find all primes less than some upperbound efficiently?

Wissam answered on April 30, 2022 Popularity 3/10 Helpfulness 8/10

answer How to find all primes less than some upperbound efficiently?

How to find all primes less than some upperbound efficiently?

Comment

"""
Implementation of the "Sieve of Eratosthenes" 
algorithm.
It aims at finding all primes that are less 
than or equal to a certain upperbound, 
denoted by n. 
Time complexity: O(n log log n) 
Space complexity: O(n)
"""
import math

def findPrimes(n):
    # Only 1 prime <= 2
    if n <= 2:
        return [2]
    """
    Initialize numbers[0] and numbers[1] as False
    because 0 and 1 are not prime.
    Set numbers[2] through numbers[n-1] to True
    When we find a divisor for one of them, set
    it to False
    """
    numbers = [False, False] + [True] * (n - 1)
    sqrtN = int(math.sqrt(n))
    for p in range(2, sqrtN + 1):
        if numbers[p]:
            # Set all multiples of p to false
            # because they are not prime.
            for multiple in range(p * p, n+1, p):
                numbers[multiple] = False
    # put all primes in a list
    result = []
    for p in range(n+1):
        if numbers[p]:
            result.append(p)
    return result

print(findPrimes(13))  # [2, 3, 5, 7, 11, 13]
print(findPrimes(19))  # [2, 3, 5, 7, 11, 13, 17, 19]

Popularity 3/10 Helpfulness 8/10 Language python

Source: Grepper

Tags: find less primes python upperbound

Link to this answer
Share Copy Link

Contributed on Apr 30 2022

Wissam

0 Answers Avg Quality 2/10

Continue with Google

By continuing, I agree that I have read and agree to Greppers's Terms of Service and Privacy Policy.

How to find all primes less than some upperbound efficiently?

Contents

More Related Answers

How to find all primes less than some upperbound efficiently?

Grepper

Documentation

Social

Legal

Contact

Oops, You will need to install Grepper and log-in to perform this action.