





"""simple docstring"""
lowerCamelCase_          =	{hex(i)[2:]: i for i in range(1_6)}  # Use [:2] to strip off the leading '0x'



def   __lowerCamelCase     (							a_  :	str							)    ->   int:
      __SCREAMING_SNAKE_CASE     :Optional[Any]	       =						hex_string.strip().lower()
      if not hex_string:
            raise ValueError('''Empty string was passed to the function'''							)
      __SCREAMING_SNAKE_CASE     :Any	       =						hex_string[0] == '''-'''
      if is_negative:
            __SCREAMING_SNAKE_CASE     :Dict	       =						hex_string[1:]
      if not all(char in hex_table for char in hex_string							):
            raise ValueError('''Non-hexadecimal value was passed to the function'''							)
      __SCREAMING_SNAKE_CASE     :Any	       =						0
      for char in hex_string:
            __SCREAMING_SNAKE_CASE     :int	       =						16 * decimal_number + hex_table[char]
      return -decimal_number if is_negative else decimal_number


if __name__ == "__main__":
  from doctest import testmod

  testmod()






"""simple docstring"""
import math
from collections.abc import Generator



def   __lowerCamelCase     (							a_  :	int							)    ->   Generator[int, None, None]:
      __SCREAMING_SNAKE_CASE     :Generator	       =						(i for i in range(1				,     (max_n + 1)							))
      for i in (n for n in numbers if n > 1):
            for j in range(2				,     a_							):
                  if (i % j) == 0:
                        break
            else:
                  yield i



def   __lowerCamelCase     (							a_  :	int							)    ->   Generator[int, None, None]:
      __SCREAMING_SNAKE_CASE     :Generator	       =						(i for i in range(1				,     (max_n + 1)							))
      for i in (n for n in numbers if n > 1):
            # only need to check for factors up to sqrt(i)
            __SCREAMING_SNAKE_CASE     :Tuple	       =						int(math.sqrt(a_							)							) + 1
            for j in range(2				,     a_							):
                  if (i % j) == 0:
                        break
            else:
                  yield i



def   __lowerCamelCase     (							a_  :	int							)    ->   Generator[int, None, None]:
      __SCREAMING_SNAKE_CASE     :Generator	       =						(i for i in range(1				,     (max_n + 1)				,     2							))
      # It's useless to test even numbers as they will not be prime
      if max_n > 2:
            yield 2  # Because 2 will not be tested, it's necessary to yield it now
      for i in (n for n in numbers if n > 1):
            __SCREAMING_SNAKE_CASE     :int	       =						int(math.sqrt(a_							)							) + 1
            for j in range(3				,     a_				,     2							):
                  # As we removed the even numbers, we don't need them now
                  if (i % j) == 0:
                        break
            else:
                  yield i



def   __lowerCamelCase     (							)    ->   Union[str, Any]:
      from timeit import timeit

      __SCREAMING_SNAKE_CASE     :Optional[Any]	       =						'''from __main__ import slow_primes, primes, fast_primes'''
      print(timeit('''slow_primes(1_000_000_000_000)'''				,     setup=a_				,     number=1_00_00_00							)							)
      print(timeit('''primes(1_000_000_000_000)'''				,     setup=a_				,     number=1_00_00_00							)							)
      print(timeit('''fast_primes(1_000_000_000_000)'''				,     setup=a_				,     number=1_00_00_00							)							)


if __name__ == "__main__":
  lowerCamelCase_          =	int(input("Calculate primes up to:\n>> ").strip())
  for ret in primes(number):
    print(ret)
  benchmark()