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60 lines
1.3 KiB
Python
60 lines
1.3 KiB
Python
#!/usr/bin/env python3
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"""
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module to operations with prime numbers
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"""
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import math
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def is_prime(number: int) -> bool:
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"""Checks to see if a number is a prime in O(sqrt(n)).
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A number is prime if it has exactly two factors: 1 and itself.
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>>> is_prime(0)
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False
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>>> is_prime(1)
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False
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>>> is_prime(2)
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True
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>>> is_prime(3)
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True
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>>> is_prime(27)
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False
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>>> is_prime(87)
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False
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>>> is_prime(563)
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True
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>>> is_prime(2999)
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True
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>>> is_prime(67483)
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False
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"""
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# precondition
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assert isinstance(number, int) and (
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number >= 0
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), "'number' must been an int and positive"
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if 1 < number < 4:
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# 2 and 3 are primes
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return True
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elif number < 2 or not number % 2:
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# Negatives, 0, 1 and all even numbers are not primes
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return False
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odd_numbers = range(3, int(math.sqrt(number) + 1), 2)
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return not any(not number % i for i in odd_numbers)
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def next_prime(value, factor=1, **kwargs):
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value = factor * value
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first_value_val = value
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while not is_prime(value):
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value += 1 if not ("desc" in kwargs and kwargs["desc"] is True) else -1
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if value == first_value_val:
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return next_prime(value + 1, **kwargs)
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return value
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