

import math



def        lowerCAmelCase__				(						SCREAMING_SNAKE_CASE_:				List[Any]   )      ->   List[str]:




				'''simple docstring'''





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

				# All primes number are in format of 6k +/- 1
				for i in range(5						,							int(math.sqrt(__A   ) + 1   )						,							6   ):
								if number % i == 0 or number % (i + 2) == 0:
												return False
				return True



def        lowerCAmelCase__				(						SCREAMING_SNAKE_CASE_:				Tuple = 0.1   )      ->   Dict:




				'''simple docstring'''





				A__          =      3
				A__          =      3

				while primes / (2 * j - 1) >= ratio:
								for i in range(j * j + j + 1						,							(j + 2) * (j + 2)						,							j + 1   ):
												primes += is_prime(__A   )
								j += 2
				return j


if __name__ == "__main__":
	import doctest

	doctest.testmod()






'''simple docstring'''





from __future__ import annotations




def lowerCAmelCase    (__A):



     """simple docstring"""



     _a           =    2
     _a           =    []
     while i * i <= n:
          if n % i:
               i += 1
          else:
               n //= i
               factors.append(__A)
     if n > 1:
          factors.append(__A)
     return factors


if __name__ == "__main__":
  import doctest

  doctest.testmod()



