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from math import floor, sqrt
from itertools import count
def is_prime(number):
if number == 1:
return False
if number == 2:
return True
if number > 2 and number % 2 == 0:
return False
boundary = floor(sqrt(number)) + 1
for div in range(3, boundary, 2):
if number % div == 0:
return False
return True
def primes_until(max_range):
for x in range(2, max_range):
if is_prime(x):
yield x
def primes_loop():
for i in count(2):
if is_prime(i):
yield i
def get_prime_factors(num):
factors = []
while num > 1:
for i in primes_loop():
if num % i == 0:
factors.append(i)
num = num // i
break
return factors
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