





'''simple docstring'''


from math import isqrt, loga


def 	__a(SCREAMING_SNAKE_CASE_  :					int    ):



    '''simple docstring'''





    _lowerCAmelCase				=      [True] * max_number
    for i in range(2		,       isqrt(max_number - 1    ) + 1    ):
        if is_prime[i]:
            for j in range(i**2		,       SCREAMING_SNAKE_CASE_		,       SCREAMING_SNAKE_CASE_    ):
                _lowerCAmelCase				=      False

    return [i for i in range(2		,       SCREAMING_SNAKE_CASE_    ) if is_prime[i]]


def 	__a(SCREAMING_SNAKE_CASE_  :					int = 800800		,       SCREAMING_SNAKE_CASE_  :					int = 800800    ):



    '''simple docstring'''





    _lowerCAmelCase				=      degree * loga(SCREAMING_SNAKE_CASE_    )
    _lowerCAmelCase				=      int(SCREAMING_SNAKE_CASE_    )
    _lowerCAmelCase				=      calculate_prime_numbers(SCREAMING_SNAKE_CASE_    )

    _lowerCAmelCase				=      0
    _lowerCAmelCase				=      0
    _lowerCAmelCase				=      len(SCREAMING_SNAKE_CASE_    ) - 1
    while left < right:
        while (
            prime_numbers[right] * loga(prime_numbers[left]    )
            + prime_numbers[left] * loga(prime_numbers[right]    )
            > upper_bound
        ):
            right -= 1
        hybrid_integers_count += right - left
        left += 1

    return hybrid_integers_count


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









'''simple docstring'''


def 	__a(SCREAMING_SNAKE_CASE_  :					str		,       SCREAMING_SNAKE_CASE_  :					bool = False    ):



    '''simple docstring'''





    if not isinstance(SCREAMING_SNAKE_CASE_		,       SCREAMING_SNAKE_CASE_    ):
        _lowerCAmelCase				=      F'''Expected string as input, found {type(SCREAMING_SNAKE_CASE_    )}'''
        raise ValueError(SCREAMING_SNAKE_CASE_    )
    if not isinstance(SCREAMING_SNAKE_CASE_		,       SCREAMING_SNAKE_CASE_    ):
        _lowerCAmelCase				=      F'''Expected boolean as use_pascal parameter, found {type(SCREAMING_SNAKE_CASE_    )}'''
        raise ValueError(SCREAMING_SNAKE_CASE_    )

    _lowerCAmelCase				=      input_str.split("_"    )

    _lowerCAmelCase				=      0 if use_pascal else 1

    _lowerCAmelCase				=      words[start_index:]

    _lowerCAmelCase				=      [word[0].upper() + word[1:] for word in words_to_capitalize]

    _lowerCAmelCase				=      "" if use_pascal else words[0]

    return "".join([initial_word, *capitalized_words]    )


if __name__ == "__main__":
       from doctest import testmod

       testmod()


