

import itertools
import math



def 					lowerCAmelCase__							(	SCREAMING_SNAKE_CASE_:							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(SCREAMING_SNAKE_CASE_      ) + 1      )	,       6      ):
								if number % i == 0 or number % (i + 2) == 0:
												return False
				return True



def 					lowerCAmelCase__							(	)			->      Union[str, Any]:




				'''simple docstring'''





				A__        =			2
				while True:
								if is_prime(SCREAMING_SNAKE_CASE_      ):
												yield num
								num += 1



def 					lowerCAmelCase__							(	SCREAMING_SNAKE_CASE_:							int = 1_0_0_0_1      )			->      int:




				'''simple docstring'''





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


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




import math

lowerCAmelCase__	   = 1_0
lowerCAmelCase__	   = 7
lowerCAmelCase__	   = BALLS_PER_COLOUR * NUM_COLOURS



def 					lowerCAmelCase__							(	SCREAMING_SNAKE_CASE_:							int = 2_0      )			->      str:




				'''simple docstring'''





				A__        =			math.comb(SCREAMING_SNAKE_CASE_	,       SCREAMING_SNAKE_CASE_      )
				A__        =			math.comb(NUM_BALLS - BALLS_PER_COLOUR	,       SCREAMING_SNAKE_CASE_      )

				A__        =			NUM_COLOURS * (1 - missing_colour / total)

				return F'{result:.9f}'


if __name__ == "__main__":
	print(solution(2_0))

