prime_numbers.py

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

importmath


defis_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
assertisinstance(number, int) and (number>=0), (
"'number' must been an int and positive"
 )

if1<number<4:
# 2 and 3 are primes
returnTrue
elifnumber<2ornotnumber%2:
# Negatives, 0, 1 and all even numbers are not primes
returnFalse

odd_numbers=range(3, int(math.sqrt(number) +1), 2)
returnnotany(notnumber%iforiinodd_numbers)


defnext_prime(value, factor=1, **kwargs):
value=factor*value
first_value_val=value

whilenotis_prime(value):
value+=1ifnot ("desc"inkwargsandkwargs["desc"] isTrue) else-1

ifvalue==first_value_val:
returnnext_prime(value+1, **kwargs)
returnvalue