
from math import sqrt



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



def  UpperCamelCase					(							lowerCAmelCase__ = 1_0001	):
					'''simple docstring'''
					lowercase					=		0
					lowercase					=		1
					while count != nth and number < 3:
										number += 1
										if is_prime(lowerCAmelCase__	):
															count += 1
					while count != nth:
										number += 2
										if is_prime(lowerCAmelCase__	):
															count += 1
					return number


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








def  UpperCamelCase					(							lowerCAmelCase__ = 1000	):
					'''simple docstring'''
					lowercase					=		-1
					lowercase					=		0
					for a in range(1				,    n // 3	):
										# Solving the two equations a**2+b**2=c**2 and a+b+c=N eliminating c
										lowercase					=		(n * n - 2 * a * n) // (2 * n - 2 * a)
										lowercase					=		n - a - b
										if c * c == (a * a + b * b):
															lowercase					=		a * b * c
															if candidate >= product:
																				lowercase					=		candidate
					return product


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




