

"""simple docstring"""




import warnings
from collections.abc import Callable
from typing import Any

import numpy
from matplotlib import pyplot

__A	:       List[Any]        =						0.25 + 0.0J
__A	:       Tuple        =						-0.4 + 0.6J
__A	:       List[Any]        =						-0.1 + 0.651J
__A	:       Union[str, Any]        =						-2.0
__A	:       Dict        =						56
__A	:       List[Any]        =						2.0
__A	:       Optional[Any]        =						6_66
def   __SCREAMING_SNAKE_CASE		(		lowercase__     ,				lowercase__ ):
					"""simple docstring"""
					return numpy.exp(lowercase__ ) + c_parameter
def   __SCREAMING_SNAKE_CASE		(		lowercase__     ,				lowercase__ ):
					"""simple docstring"""
					return z_values * z_values + c_parameter
def   __SCREAMING_SNAKE_CASE		(		lowercase__     ,				lowercase__ ):
					"""simple docstring"""
					A     =   numpy.linspace(-window_size     ,				lowercase__     ,				lowercase__ )
					A     =   x.reshape((nb_pixels, 1) )
					A     =   numpy.linspace(-window_size     ,				lowercase__     ,				lowercase__ )
					A     =   y.reshape((1, nb_pixels) )
					return x + 1.0J * y
def   __SCREAMING_SNAKE_CASE		(		lowercase__     ,				lowercase__     ,				lowercase__     ,				lowercase__     ,				lowercase__ = None     ,				):
					"""simple docstring"""
					A     =   z_a.astype("complex64" )
					for _ in range(lowercase__ ):
										A     =   eval_function(lowercase__     ,				lowercase__ )
										if infinity is not None:
															numpy.nan_to_num(lowercase__     ,				copy=lowercase__     ,				nan=lowercase__ )
															A     =   infinity
					return z_n
def   __SCREAMING_SNAKE_CASE		(		lowercase__     ,				lowercase__     ,				lowercase__     ,				lowercase__     ,				):
					"""simple docstring"""
					A     =   (abs(lowercase__ )).transpose()
					A     =   abs_z_final[::-1, :]
					pyplot.matshow(abs_z_final < escape_radius )
					pyplot.title(F"""Julia set of ${function_label}$, $c={function_params}$""" )
					pyplot.show()
def   __SCREAMING_SNAKE_CASE		(		):
					"""simple docstring"""
					warnings.filterwarnings(
					    "ignore"     ,				category=lowercase__     ,				message="overflow encountered in multiply" )
					warnings.filterwarnings(
					    "ignore"     ,				category=lowercase__     ,				message="invalid value encountered in multiply"     ,				)
					warnings.filterwarnings(
					    "ignore"     ,				category=lowercase__     ,				message="overflow encountered in absolute" )
					warnings.filterwarnings(
					    "ignore"     ,				category=lowercase__     ,				message="overflow encountered in exp" )


if __name__ == "__main__":
	__A	:       Optional[Any]        =						prepare_grid(window_size, nb_pixels)

	ignore_overflow_warnings()  # See file header for explanations

	__A	:       Optional[Any]        =						24
	__A	:       Optional[int]        =						2 * abs(c_cauliflower) + 1
	__A	:       int        =						iterate_function(
	    eval_quadratic_polynomial,
	    c_cauliflower,
	    nb_iterations,
	    z_a,
	    infinity=1.1 * escape_radius,
	)
	show_results('z^2+c', c_cauliflower, escape_radius, z_final)

	__A	:       Optional[Any]        =						64
	__A	:       List[str]        =						2 * abs(c_polynomial_a) + 1
	__A	:       Union[str, Any]        =						iterate_function(
	    eval_quadratic_polynomial,
	    c_polynomial_a,
	    nb_iterations,
	    z_a,
	    infinity=1.1 * escape_radius,
	)
	show_results('z^2+c', c_polynomial_a, escape_radius, z_final)

	__A	:       Any        =						1_61
	__A	:       Union[str, Any]        =						2 * abs(c_polynomial_a) + 1
	__A	:       int        =						iterate_function(
	    eval_quadratic_polynomial,
	    c_polynomial_a,
	    nb_iterations,
	    z_a,
	    infinity=1.1 * escape_radius,
	)
	show_results('z^2+c', c_polynomial_a, escape_radius, z_final)

	__A	:       str        =						12
	__A	:       List[str]        =						1_00_00.0
	__A	:       Dict        =						iterate_function(
	    eval_exponential,
	    c_exponential,
	    nb_iterations,
	    z_a + 2,
	    infinity=1.0E10,
	)
	show_results('e^z+c', c_exponential, escape_radius, z_final)






"""simple docstring"""




import math
from collections.abc import Generator



def 				__a       (			_lowercase						):







					"""simple docstring"""





					lowerCamelCase__		:   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							, _lowercase						):
															if (i % j) == 0:
																				break
										else:
															yield i



def 				__a       (			_lowercase						):







					"""simple docstring"""





					lowerCamelCase__		:   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)
										lowerCamelCase__		:   Tuple  				=					int(math.sqrt(_lowercase						)						) + 1
										for j in range(2							, _lowercase						):
															if (i % j) == 0:
																				break
										else:
															yield i



def 				__a       (			_lowercase						):







					"""simple docstring"""





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



def 				__a       (			):







					"""simple docstring"""





					from timeit import timeit

					lowerCamelCase__		:   Any  				=					'''from __main__ import slow_primes, primes, fast_primes'''
					print(timeit('''slow_primes(1_000_000_000_000)'''							, setup=_lowercase							, number=1000000						)						)
					print(timeit('''primes(1_000_000_000_000)'''							, setup=_lowercase							, number=1000000						)						)
					print(timeit('''fast_primes(1_000_000_000_000)'''							, setup=_lowercase							, number=1000000						)						)


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






