Python/data_structures/hashing/number_theory/prime_numbers.py

#!/usr/bin/env python3
"""
    module to operations with prime numbers
"""

import math


def is_prime(number: int) -> bool:
    """Checks to see if a number is a prime in O(sqrt(n)).

    A number is prime if it has exactly two factors: 1 and itself.

    >>> is_prime(0)
    False
    >>> is_prime(1)
    False
    >>> is_prime(2)
    True
    >>> is_prime(3)
    True
    >>> is_prime(27)
    False
    >>> is_prime(87)
    False
    >>> is_prime(563)
    True
    >>> is_prime(2999)
    True
    >>> is_prime(67483)
    False
    """

    # precondition
    assert isinstance(number, int) and (
        number >= 0
    ), "'number' must been an int and positive"

    if 1 < number < 4:
        # 2 and 3 are primes
        return True
    elif number < 2 or not number % 2:
        # Negatives, 0, 1 and all even numbers are not primes
        return False

    odd_numbers = range(3, int(math.sqrt(number) + 1), 2)
    return not any(not number % i for i in odd_numbers)


def next_prime(value, factor=1, **kwargs):
    value = factor * value
    first_value_val = value

    while not is_prime(value):
        value += 1 if not ("desc" in kwargs.keys() and kwargs["desc"] is True) else -1

    if value == first_value_val:
        return next_prime(value + 1, **kwargs)
    return value