
"""simple docstring"""

from __future__ import annotations

import math




def      lowercase__    (       lowerCAmelCase					:       int			)			->   bool:






    """simple docstring"""




    if 1 < number < 4:
        # 2 and 3 are primes
        return True
    elif number < 2 or number % 2 == 0 or number % 3 == 0:
        # Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
        return False

    # All primes number are in format of 6k +/- 1
    for i in range(5			,					int(math.sqrt(lowerCAmelCase			) + 1			)			,					6			):
        if number % i == 0 or number % (i + 2) == 0:
            return False
    return True


SCREAMING_SNAKE_CASE_            =    [num for num in range(3, 10_0001, 2) if not is_prime(num)]




def      lowercase__    (       lowerCAmelCase					:       int			)			->   list[int]:






    """simple docstring"""




    if not isinstance(lowerCAmelCase			,					lowerCAmelCase			):
        raise ValueError('n must be an integer'			)
    if n <= 0:
        raise ValueError('n must be >= 0'			)

    UpperCAmelCase          =       []
    for num in range(len(lowerCAmelCase			)			):
        UpperCAmelCase          =       0
        while 2 * i * i <= odd_composites[num]:
            UpperCAmelCase          =       odd_composites[num] - 2 * i * i
            if is_prime(lowerCAmelCase			):
                break
            i += 1
        else:
            list_nums.append(odd_composites[num]			)
            if len(lowerCAmelCase			) == n:
                return list_nums

    return []




def      lowercase__    (       )			->   int:






    """simple docstring"""




    return compute_nums(1			)[0]


if __name__ == "__main__":
   print(F'{solution() = }')





"""simple docstring"""

from math import asin, atan, cos, radians, sin, sqrt, tan

SCREAMING_SNAKE_CASE_            =    6_3_7_8_1_3_7.0
SCREAMING_SNAKE_CASE_            =    6_3_5_6_7_5_2.3_1_4_2_4_5
SCREAMING_SNAKE_CASE_            =    637_8137




def      lowercase__    (       lowerCAmelCase					:       float			,					lowerCAmelCase					:       float			,					lowerCAmelCase					:       float			,					lowerCAmelCase					:       float			)			->   float:






    """simple docstring"""




    UpperCAmelCase          =       (AXIS_A - AXIS_B) / AXIS_A
    UpperCAmelCase          =       atan((1 - flattening) * tan(radians(lowerCAmelCase			)			)			)
    UpperCAmelCase          =       atan((1 - flattening) * tan(radians(lowerCAmelCase			)			)			)
    UpperCAmelCase          =       radians(lowerCAmelCase			)
    UpperCAmelCase          =       radians(lowerCAmelCase			)
    # Equation
    UpperCAmelCase          =       sin((phi_a - phi_a) / 2			)
    UpperCAmelCase          =       sin((lambda_a - lambda_a) / 2			)
    # Square both values
    sin_sq_phi *= sin_sq_phi
    sin_sq_lambda *= sin_sq_lambda
    UpperCAmelCase          =       sqrt(sin_sq_phi + (cos(lowerCAmelCase			) * cos(lowerCAmelCase			) * sin_sq_lambda)			)
    return 2 * RADIUS * asin(lowerCAmelCase			)


if __name__ == "__main__":
   import doctest

   doctest.testmod()



