from __future__ import annotations

A  :	int         =							[True] * 1_00_00_01
A  :	Optional[int]         =							2
while i * i <= 1_00_00_00:
      if seive[i]:
            for j in range(i * i, 1_00_00_01, i):
                  A  :	Optional[int]         =							False
      i += 1


def   a__			(		__UpperCamelCase					):
      return seive[n]


def   a__			(		__UpperCamelCase					):
      return any(digit in "02468" for digit in str(lowercase_					)					)


def   a__			(		__UpperCamelCase = 1_0_0_0_0_0_0					):
      SCREAMING_SNAKE_CASE_    =	[2]  # result already includes the number 2.
      for num in range(3  ,   limit + 1  ,   2					):
            if is_prime(lowercase_					) and not contains_an_even_digit(lowercase_					):
                  SCREAMING_SNAKE_CASE_    =	str(lowercase_					)
                  SCREAMING_SNAKE_CASE_    =	[int(str_num[j:] + str_num[:j]					) for j in range(len(lowercase_					)					)]
                  if all(is_prime(lowercase_					) for i in list_nums					):
                        result.append(lowercase_					)
      return result


def   a__			(		):
      return len(find_circular_primes()					)


if __name__ == "__main__":
      print(f"{len(find_circular_primes()) = }")








from math import sqrt

import numpy as np
from sympy import symbols

# Coefficient
# Speed of light (m/s)
_lowerCamelCase      :						str							=  299792458

# Symbols
_lowerCamelCase			,     _lowerCamelCase			,     _lowerCamelCase			,     _lowerCamelCase      :						int							=  symbols("""ct x y z""")







def SCREAMING_SNAKE_CASE							(			lowercase_		)  ->			float:



       """simple docstring"""

       if velocity > c:
              raise ValueError('''Speed must not exceed light speed 299,792,458 [m/s]!'''		)
       elif velocity < 1:
              # Usually the speed should be much higher than 1 (c order of magnitude)
              raise ValueError('''Speed must be greater than or equal to 1!'''		)

       return velocity / c







def SCREAMING_SNAKE_CASE							(			lowercase_		)  ->			float:



       """simple docstring"""

       return 1 / sqrt(1 - beta(lowercase_		) ** 2		)







def SCREAMING_SNAKE_CASE							(			lowercase_		)  ->			np.ndarray:



       """simple docstring"""

       return np.array(
           [
               [gamma(lowercase_		), -gamma(lowercase_		) * beta(lowercase_		), 0, 0],
               [-gamma(lowercase_		) * beta(lowercase_		), gamma(lowercase_		), 0, 0],
               [0, 0, 1, 0],
               [0, 0, 0, 1],
           ]		)







def SCREAMING_SNAKE_CASE							(			lowercase_					,							lowercase_ = None		)  ->			np.ndarray:



       """simple docstring"""

       if event is None:
              A__ 					=       np.array([ct, x, y, z]		)  # Symbolic four vector
       else:
              event[0] *= c  # x0 is ct (speed of light * time)

       return transformation_matrix(lowercase_		) @ event


if __name__ == "__main__":
  import doctest

  doctest.testmod()

  # Example of symbolic vector:
  _lowerCamelCase      :						Tuple							=  transform(29979245)
  print("""Example of four vector: """)
  print(F'''ct\' = {four_vector[0]}''')
  print(F'''x\' = {four_vector[1]}''')
  print(F'''y\' = {four_vector[2]}''')
  print(F'''z\' = {four_vector[3]}''')

  # Substitute symbols with numerical values
  _lowerCamelCase      :						int							=  {ct: c, x: 1, y: 1, z: 1}
  _lowerCamelCase      :						Any							=  [four_vector[i].subs(sub_dict) for i in range(4)]

  print(F'''\n{numerical_vector}''')


