import math
from collections.abc import Generator

def      lowercase_							(     _lowerCamelCase				:			int):
    lowercase__					:  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      lowercase_							(     _lowerCamelCase				:			int):
    lowercase__					:  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)
        lowercase__					:  List[str]          =							int(math.sqrt(_A)) + 1
        for j in range(2						,      _A):
            if (i % j) == 0:
                break
        else:
            yield i

def      lowercase_							(     _lowerCamelCase				:			int):
    lowercase__					:  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):
        lowercase__					:  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      lowercase_							(     ):
    from timeit import timeit

    lowercase__					:  Tuple          =							'from __main__ import slow_primes, primes, fast_primes'
    print(timeit("slow_primes(1_000_000_000_000)"						,      setup=_A						,      number=100_0000))
    print(timeit("primes(1_000_000_000_000)"						,      setup=_A						,      number=100_0000))
    print(timeit("fast_primes(1_000_000_000_000)"						,      setup=_A						,      number=100_0000))


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







'''simple docstring'''




from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_sentencepiece_available, is_tokenizers_available


_lowerCAmelCase	:		Dict		  =						{}

try:
				if not is_sentencepiece_available():
								raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
				pass
else:
				_lowerCAmelCase	:		Union[str, Any]		  =						['BarthezTokenizer']

try:
				if not is_tokenizers_available():
								raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
				pass
else:
				_lowerCAmelCase	:		Union[str, Any]		  =						['BarthezTokenizerFast']


if TYPE_CHECKING:
				try:
								if not is_sentencepiece_available():
												raise OptionalDependencyNotAvailable()
				except OptionalDependencyNotAvailable:
								pass
				else:
								from .tokenization_barthez import BarthezTokenizer

				try:
								if not is_tokenizers_available():
												raise OptionalDependencyNotAvailable()
				except OptionalDependencyNotAvailable:
								pass
				else:
								from .tokenization_barthez_fast import BarthezTokenizerFast

else:
				import sys

				_lowerCAmelCase	:		List[str]		  =						_LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)
