Find prime factorizations of numbers, with small optimizations

prime_factorization.py

import math

def require_int(n):
  if not type(n) is int:
    raise TypeError('argument must have type int; got {} which has type {}'.format(n, type(n).__name__))

def require_non_negative_int(n):
  require_int(n)
  if n < 0:
    raise ValueError('argument must be an int >= 0; got {}'.format(n))

def is_prime(n):
  require_non_negative_int(n)
  if n == 0:
    return False
  return not any(d for d in range(2, math.floor(math.sqrt(n)) + 1) if n % d == 0)

KNOWN_PRIMES_ORDERED_CACHE = []

def primes_under(n):
  "Generate a sequence of prime numbers less than n"
  require_non_negative_int(n)
  for p in KNOWN_PRIMES_ORDERED_CACHE:
    if p < n:
      yield p
    else:
      break
  continue_at = KNOWN_PRIMES_ORDERED_CACHE[-1] + 1 if KNOWN_PRIMES_ORDERED_CACHE else 2
  for d in range(continue_at, n):
    if is_prime(d):
      KNOWN_PRIMES_ORDERED_CACHE.append(d)
      yield d

def prime_factors(n):
  "Return a list of prime integers, that multiplied together, result in n"
  require_non_negative_int(n)
  factor_seek_limit = math.floor(math.sqrt(n)) + 1
  current = n
  factors = []
  while not is_prime(current):
    for f in primes_under(factor_seek_limit):
      if current % f == 0:
        factors.append(f)
        current //= f
        break
  factors.append(current)
  return factors