prime_number_generation.py

'''
Sieve is good for pre-generating list of primes, so that you can check quickly if a number is prime or not.
If you're checking if a single number is a prime or not, use the looping method
'''

import math


def generate_primes_sieve(n):
    non_primes = set()
    for i in range(2, n+1):
        if i not in non_primes:
            yield i
            for j in range(i**2, n+1, i):
                non_primes.add(j)


def get_primes_sieve(n):
    primes = []
    non_primes = set()
    for i in range(2, n+1):
        if i not in non_primes:
            primes.append(i)
            for j in range(i**2, n+1, i):
                non_primes.add(j)
    return primes


def is_prime_sieve(n):
    if n < 2:
        return False
    for prime_number in generate_primes_sieve(int(math.sqrt(n))):
        if n % prime_number == 0:
            return False
    return True


def is_prime_loop(n):
    if n < 2:
        return False
    for x in range(2, int(math.sqrt(n))+1):
        if n % x == 0:
            return False
    return True