



'''simple docstring'''





import itertools
import math




def 							lowerCamelCase	(					_snake_case	:    int							):





    '''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(_snake_case							) + 1							)  ,6							):
        if number % i == 0 or number % (i + 2) == 0:
            return False
    return True




def 							lowerCamelCase	(					):





    '''simple docstring'''


    lowercase__									=    2
    while True:
        if is_prime(_snake_case							):
            yield num
        num += 1




def 							lowerCamelCase	(					_snake_case	:    int = 10_001							):





    '''simple docstring'''


    return next(itertools.islice(prime_generator()  ,nth - 1  ,_snake_case							)							)


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









'''simple docstring'''





def 							lowerCamelCase	(					_snake_case	:    list							):





    '''simple docstring'''


    if not isinstance(_snake_case  ,_snake_case							):
        raise ValueError("Input series is not valid, valid series - [2, 4, 6]"							)
    if len(_snake_case							) == 0:
        raise ValueError("Input list must be a non empty list"							)
    if len(_snake_case							) == 1:
        return True
    lowercase__									=    series[1] - series[0]
    for index in range(len(_snake_case							) - 1							):
        if series[index + 1] - series[index] != common_diff:
            return False
    return True




def 							lowerCamelCase	(					_snake_case	:    list							):





    '''simple docstring'''


    if not isinstance(_snake_case  ,_snake_case							):
        raise ValueError("Input series is not valid, valid series - [2, 4, 6]"							)
    if len(_snake_case							) == 0:
        raise ValueError("Input list must be a non empty list"							)
    lowercase__									=    0
    for val in series:
        answer += val
    return answer / len(_snake_case							)


if __name__ == "__main__":
 import doctest

 doctest.testmod()




