Primes

primes.py

""" This module contains the following algorithms for generating primes:
    - Sieves of Eratosthenes (Optimized)
    - Sieve of Atkins
"""
from math import sqrt


def eratosthenes(lim=100):
    """
    Implements a Genuine Sieve of Eratosthenes for primes < lim

    returns: list of primes < lim
    """

    is_prime = list(True for _ in range(lim + 1))
    sqrtn = int(round(sqrt(lim)))

    for i in range(2, sqrtn + 1):
        if is_prime[i]:
            for j in range(i ** 2, lim + 1, i):
                is_prime[j] = False

    return [i for i, b in enumerate(is_prime) if b and i >= 2]

print(eratosthenes(10000))

Sieve.java

public class Sieve{
    public static void main(String[] args){
        Integer maxPrime = 10000;
        Double sqrtMaxPrime = Math.sqrt(maxPrime);
        Boolean[] isPrime = new Boolean[maxPrime+1];

        for (int i=0; i<=maxPrime; i++) {
            isPrime[i] = true;
        }
        for (int i=2; i<=sqrtMaxPrime; i++){
            if (isPrime[i]){
                for (int j=i*i; j<=maxPrime; j+= i){
                    isPrime[j] = false;
                }
            }
        }
        for (int i=2; i<=maxPrime; i++){
            if(isPrime[i]){
                System.out.println(i);
            }
        }
    }
}