




"""simple docstring"""



import math







def   _SCREAMING_SNAKE_CASE       (							lowercase_						)						->		bool:

 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(lowercase_						) + 1						)      ,			6						):
  if number % i == 0 or number % (i + 2) == 0:
   return False
 return True







def   _SCREAMING_SNAKE_CASE       (							lowercase_ = 1_00_01						)						->		int:

 try:
  A__	=    int(lowercase_						)
 except (TypeError, ValueError):
  raise TypeError("Parameter nth must be int or castable to int."						) from None
 if nth <= 0:
  raise ValueError("Parameter nth must be greater than or equal to one."						)
 A__	=    []
 A__	=    2
 while len(lowercase_						) < nth:
  if is_prime(lowercase_						):
   primes.append(lowercase_						)
   num += 1
  else:
   num += 1
 return primes[len(lowercase_						) - 1]


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











"""simple docstring"""



import random

from .binary_exp_mod import bin_exp_mod







def   _SCREAMING_SNAKE_CASE       (							lowercase_      ,			lowercase_=10_00						)						->		Optional[Any]:
 if n < 2:
  return False

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

 # this means n is odd
 A__	=    n - 1
 A__	=    0
 while d % 2 == 0:
  d /= 2
  exp += 1

 # n - 1=d*(2**exp)
 A__	=    0
 while count < prec:
  A__	=    random.randint(2      ,			n - 1						)
  A__	=    bin_exp_mod(lowercase_      ,			lowercase_      ,			lowercase_						)
  if b != 1:
   A__	=    True
   for _ in range(lowercase_						):
    if b == n - 1:
     A__	=    False
     break
    A__	=    b * b
    b %= n
   if flag:
    return False
   count += 1
 return True


if __name__ == "__main__":
      SCREAMING_SNAKE_CASE    =	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)))





