mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-11-30 16:31:08 +00:00
60 lines
1.3 KiB
Python
60 lines
1.3 KiB
Python
#!/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 and kwargs["desc"] is True) else -1
|
|
|
|
if value == first_value_val:
|
|
return next_prime(value + 1, **kwargs)
|
|
return value
|