


'''simple docstring'''


import random


def 		_lowercase (SCREAMING_SNAKE_CASE							):




     '''simple docstring'''





     __A	:       str      =							num - 1
     __A	:       int      =							0

     while s % 2 == 0:
          __A	:       Tuple      =							s // 2
          t += 1

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


def 		_lowercase (SCREAMING_SNAKE_CASE							):




     '''simple docstring'''





     if num < 2:
          return False

     __A	:       Dict      =							[
         2,
         3,
         5,
         7,
         11,
         13,
         17,
         19,
         23,
         29,
         31,
         37,
         41,
         43,
         47,
         53,
         59,
         61,
         67,
         71,
         73,
         79,
         83,
         89,
         97,
         101,
         103,
         107,
         109,
         113,
         127,
         131,
         137,
         139,
         149,
         151,
         157,
         163,
         167,
         173,
         179,
         181,
         191,
         193,
         197,
         199,
         211,
         223,
         227,
         229,
         233,
         239,
         241,
         251,
         257,
         263,
         269,
         271,
         277,
         281,
         283,
         293,
         307,
         311,
         313,
         317,
         331,
         337,
         347,
         349,
         353,
         359,
         367,
         373,
         379,
         383,
         389,
         397,
         401,
         409,
         419,
         421,
         431,
         433,
         439,
         443,
         449,
         457,
         461,
         463,
         467,
         479,
         487,
         491,
         499,
         503,
         509,
         521,
         523,
         541,
         547,
         557,
         563,
         569,
         571,
         577,
         587,
         593,
         599,
         601,
         607,
         613,
         617,
         619,
         631,
         641,
         643,
         647,
         653,
         659,
         661,
         673,
         677,
         683,
         691,
         701,
         709,
         719,
         727,
         733,
         739,
         743,
         751,
         757,
         761,
         769,
         773,
         787,
         797,
         809,
         811,
         821,
         823,
         827,
         829,
         839,
         853,
         857,
         859,
         863,
         877,
         881,
         883,
         887,
         907,
         911,
         919,
         929,
         937,
         941,
         947,
         953,
         967,
         971,
         977,
         983,
         991,
         997,
     ]

     if num in low_primes:
          return True

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

     return rabin_miller(SCREAMING_SNAKE_CASE							)


def 		_lowercase (SCREAMING_SNAKE_CASE = 1024							):




     '''simple docstring'''





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


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





'''simple docstring'''


def 		_lowercase (SCREAMING_SNAKE_CASE							):




     '''simple docstring'''





     __A	:       List[str]      =							1
     __A	:       Union[str, Any]      =							2
     while i * i <= n:
          __A	:       List[Any]      =							0
          while n % i == 0:
               n //= i
               multiplicity += 1
          n_divisors *= multiplicity + 1
          i += 1
     if n > 1:
          n_divisors *= 2
     return n_divisors


def 		_lowercase ():




     '''simple docstring'''





     __A	:       Optional[Any]      =							1
     __A	:       Dict      =							1

     while True:
          i += 1
          t_num += i

          if count_divisors(SCREAMING_SNAKE_CASE							) > 500:
               break

     return t_num


if __name__ == "__main__":
      print(solution())

