



import math
from collections.abc import Generator






def 						_lowerCAmelCase    (					__lowerCamelCase :  int  ):



 """simple docstring"""





 __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		,						__lowerCamelCase  ):
   if (i % j) == 0:
    break
  else:
   yield i






def 						_lowerCAmelCase    (					__lowerCamelCase :  int  ):



 """simple docstring"""





 __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							:     str							=						int(math.sqrt(__lowerCamelCase  )  ) + 1
  for j in range(2		,						__lowerCamelCase  ):
   if (i % j) == 0:
    break
  else:
   yield i






def 						_lowerCAmelCase    (					__lowerCamelCase :  int  ):



 """simple docstring"""





 __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							:     List[Any]							=						int(math.sqrt(__lowerCamelCase  )  ) + 1
  for j in range(3		,						__lowerCamelCase		,						2  ):
   # As we removed the even numbers, we don't need them now
   if (i % j) == 0:
    break
  else:
   yield i






def 						_lowerCAmelCase    (					):



 """simple docstring"""





 from timeit import timeit

 __SCREAMING_SNAKE_CASE							:     Union[str, Any]							=						"from __main__ import slow_primes, primes, fast_primes"
 print(timeit("slow_primes(1_000_000_000_000)"		,						setup=__lowerCamelCase		,						number=1000000  )  )
 print(timeit("primes(1_000_000_000_000)"		,						setup=__lowerCamelCase		,						number=1000000  )  )
 print(timeit("fast_primes(1_000_000_000_000)"		,						setup=__lowerCamelCase		,						number=1000000  )  )


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











'''simple docstring'''







def 			_lowerCAmelCase(      UpperCAmelCase_      :	str						) ->							str:
							lowerCAmelCase__  =   word.upper()
							lowerCAmelCase__  =   0
							lowerCAmelCase__  =   {}
							lowerCAmelCase__  =   []

							for letter in word:
														if letter not in letter_nums:
																					lowerCAmelCase__  =   str(UpperCAmelCase_						)
																					next_num += 1
														word_pattern.append(letter_nums[letter]						)
							return ".".join(UpperCAmelCase_						)


if __name__ == "__main__":
		import pprint
		import time

		_UpperCamelCase  						=			time.time()
		with open("""dictionary.txt""") as in_file:
				_UpperCamelCase  						=			in_file.read().splitlines()

		_UpperCamelCase  						=			{}
		for word in word_list:
				_UpperCamelCase  						=			get_word_pattern(word)
				if pattern in all_patterns:
						all_patterns[pattern].append(word)
				else:
						_UpperCamelCase  						=			[word]

		with open("""word_patterns.txt""", """w""") as out_file:
				out_file.write(pprint.pformat(all_patterns))

		_UpperCamelCase  						=			round(time.time() - start_time, 2)
		print(f'Done!  {len(all_patterns):,} word patterns found in {total_time} seconds.')
		# Done!  9,581 word patterns found in 0.58 seconds.





