



'''simple docstring'''






import random

from .binary_exp_mod import bin_exp_mod




def     snake_case_					(     lowerCAmelCase_       ,   lowerCAmelCase_=1000		)->		List[Any]:





       '''simple docstring'''


       if n < 2:
              return False

       if n % 2 == 0:
              return n == 2

       # this means n is odd
       _UpperCAmelCase  :						List[Any]			     = n - 1
       _UpperCAmelCase  :						Optional[Any]			     = 0
       while d % 2 == 0:
              d /= 2
              exp += 1

       # n - 1=d*(2**exp)
       _UpperCAmelCase  :						Tuple			     = 0
       while count < prec:
              _UpperCAmelCase  :						Any			     = random.randint(2       ,   n - 1		)
              _UpperCAmelCase  :						List[str]			     = bin_exp_mod(lowerCAmelCase_       ,   lowerCAmelCase_       ,   lowerCAmelCase_		)
              if b != 1:
                     _UpperCAmelCase  :						List[Any]			     = True
                     for _ in range(lowerCAmelCase_		):
                            if b == n - 1:
                                   _UpperCAmelCase  :						Optional[Any]			     = False
                                   break
                            _UpperCAmelCase  :						List[Any]			     = b * b
                            b %= n
                     if flag:
                            return False
                     count += 1
       return True


if __name__ == "__main__":
   A_							: Tuple						 =	abs(int(input("""Enter bound : """).strip()))
   print("""Here's the list of primes:""")
   print(""", """.join(str(i) for i in range(n + 1) if is_prime_big(i)))








'''simple docstring'''






from numpy import exp, pi, sqrt




def     snake_case_					(     lowerCAmelCase_       ,   lowerCAmelCase_ = 0.0       ,   lowerCAmelCase_ = 1.0		)->		int:





       '''simple docstring'''


       return 1 / sqrt(2 * pi * sigma**2		) * exp(-((x - mu) ** 2) / (2 * sigma**2)		)


if __name__ == "__main__":
   import doctest

   doctest.testmod()



