"""

Primality Test

--------------

Implementation of a Primality Test that uses a cache to improve

performance.

"""

from math import sqrt

from algorithms.math.sieve_eratosthenes import eratosthenes

CACHE_LIMIT = 10 ** 6

primes_cache_list = []

primes_cache_bool = []

def is_prime(number, cache=True):

"""

Takes `number` and determines if it is prime.

:param number: The integer to be tested for primality.

:param cache: A boolean to determine if a cache should be used to

improve performance.

:rtype: A boolean that signifies if `number` is prime.

"""

if number < 2:

return False

global primes_cache_list, primes_cache_bool

if cache and len(primes_cache_list) == 0:

primes_cache_list, primes_cache_bool = eratosthenes(

CACHE_LIMIT, return_boolean=True

)

for prime in primes_cache_list:

primes_cache_bool[prime] = True

if number < len(primes_cache_bool):

return primes_cache_bool[number]

sqrt_number = sqrt(number)

for prime in primes_cache_list:

if prime > sqrt_number:

return True

if number % prime == 0:

return False

to_check = 2

if len(primes_cache_list) > 0:

to_check = primes_cache_list[-1] + 1

while to_check <= sqrt_number:

if number % to_check == 0:

return False

to_check += 1

return True