






'''simple docstring'''



import random


def 							lowercase_				(    __A :       int			)       ->      bool:



 """simple docstring"""




 lowercase					:   Dict				  =num - 1
 lowercase					:   Union[str, Any]				  =0

 while s % 2 == 0:
  lowercase					:   Any				  =s // 2
  t += 1

 for _ in range(5			):
  lowercase					:   Any				  =random.randrange(2					,      num - 1			)
  lowercase					:   Optional[Any]				  =pow(__A					,      __A					,      __A			)
  if v != 1:
   lowercase					:   str				  =0
   while v != (num - 1):
    if i == t - 1:
     return False
    else:
     lowercase					:   List[str]				  =i + 1
     lowercase					:   Tuple				  =(v**2) % num
 return True


def 							lowercase_				(    __A :       int			)       ->      bool:



 """simple docstring"""




 if num < 2:
  return False

 lowercase					:   Any				  =[
     2,
     3,
     5,
     7,
     1_1,
     1_3,
     1_7,
     1_9,
     2_3,
     2_9,
     3_1,
     3_7,
     4_1,
     4_3,
     4_7,
     5_3,
     5_9,
     6_1,
     6_7,
     7_1,
     7_3,
     7_9,
     8_3,
     8_9,
     9_7,
     1_0_1,
     1_0_3,
     1_0_7,
     1_0_9,
     1_1_3,
     1_2_7,
     1_3_1,
     1_3_7,
     1_3_9,
     1_4_9,
     1_5_1,
     1_5_7,
     1_6_3,
     1_6_7,
     1_7_3,
     1_7_9,
     1_8_1,
     1_9_1,
     1_9_3,
     1_9_7,
     1_9_9,
     2_1_1,
     2_2_3,
     2_2_7,
     2_2_9,
     2_3_3,
     2_3_9,
     2_4_1,
     2_5_1,
     2_5_7,
     2_6_3,
     2_6_9,
     2_7_1,
     2_7_7,
     2_8_1,
     2_8_3,
     2_9_3,
     3_0_7,
     3_1_1,
     3_1_3,
     3_1_7,
     3_3_1,
     3_3_7,
     3_4_7,
     3_4_9,
     3_5_3,
     3_5_9,
     3_6_7,
     3_7_3,
     3_7_9,
     3_8_3,
     3_8_9,
     3_9_7,
     4_0_1,
     4_0_9,
     4_1_9,
     4_2_1,
     4_3_1,
     4_3_3,
     4_3_9,
     4_4_3,
     4_4_9,
     4_5_7,
     4_6_1,
     4_6_3,
     4_6_7,
     4_7_9,
     4_8_7,
     4_9_1,
     4_9_9,
     5_0_3,
     5_0_9,
     5_2_1,
     5_2_3,
     5_4_1,
     5_4_7,
     5_5_7,
     5_6_3,
     5_6_9,
     5_7_1,
     5_7_7,
     5_8_7,
     5_9_3,
     5_9_9,
     6_0_1,
     6_0_7,
     6_1_3,
     6_1_7,
     6_1_9,
     6_3_1,
     6_4_1,
     6_4_3,
     6_4_7,
     6_5_3,
     6_5_9,
     6_6_1,
     6_7_3,
     6_7_7,
     6_8_3,
     6_9_1,
     7_0_1,
     7_0_9,
     7_1_9,
     7_2_7,
     7_3_3,
     7_3_9,
     7_4_3,
     7_5_1,
     7_5_7,
     7_6_1,
     7_6_9,
     7_7_3,
     7_8_7,
     7_9_7,
     8_0_9,
     8_1_1,
     8_2_1,
     8_2_3,
     8_2_7,
     8_2_9,
     8_3_9,
     8_5_3,
     8_5_7,
     8_5_9,
     8_6_3,
     8_7_7,
     8_8_1,
     8_8_3,
     8_8_7,
     9_0_7,
     9_1_1,
     9_1_9,
     9_2_9,
     9_3_7,
     9_4_1,
     9_4_7,
     9_5_3,
     9_6_7,
     9_7_1,
     9_7_7,
     9_8_3,
     9_9_1,
     9_9_7,
 ]

 if num in low_primes:
  return True

 for prime in low_primes:
  if (num % prime) == 0:
   return False

 return rabin_miller(__A			)


def 							lowercase_				(    __A :       int = 1_0_2_4			)       ->      int:



 """simple docstring"""




 while True:
  lowercase					:   Tuple				  =random.randrange(2 ** (keysize - 1)					,      2 ** (keysize)			)
  if is_prime_low_num(__A			):
   return num


if __name__ == "__main__":
      SCREAMING_SNAKE_CASE						=	generate_large_prime()
      print(('Prime number:', num))
      print(('is_prime_low_num:', is_prime_low_num(num)))











'''simple docstring'''



def 							lowercase_				(    __A :       int = 6_0_0_8_5_1_4_7_5_1_4_3			)       ->      int:



 """simple docstring"""




 try:
  lowercase					:   Any				  =int(__A			)
 except (TypeError, ValueError):
  raise TypeError('''Parameter n must be int or castable to int.'''			)
 if n <= 0:
  raise ValueError('''Parameter n must be greater than or equal to one.'''			)
 lowercase					:   Optional[Any]				  =1
 lowercase					:   Dict				  =2
 while i * i <= n:
  while n % i == 0:
   lowercase					:   Optional[int]				  =i
   n //= i
  i += 1
 if n > 1:
  lowercase					:   Dict				  =n
 return int(__A			)


if __name__ == "__main__":
      print(f"""{solution() = }""")



