




import math







def      _a				(						SCREAMING_SNAKE_CASE_							:    int					):

					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      _a				(						SCREAMING_SNAKE_CASE_							:    float = 0.1					):
					__lowerCAmelCase           =	3
					__lowerCAmelCase           =	3

					while primes / (2 * j - 1) >= ratio:
										for i in range(j * j + j + 1				,				(j + 2) * (j + 2)				,				j + 1					):
															primes += is_prime(SCREAMING_SNAKE_CASE_					)
										j += 2
					return j


if __name__ == "__main__":
							import doctest

							doctest.testmod()










from __future__ import annotations







def      _a				(						SCREAMING_SNAKE_CASE_							:    float				,				SCREAMING_SNAKE_CASE_							:    float				,				SCREAMING_SNAKE_CASE_							:    float				,				):
					if (electron_conc, hole_conc, intrinsic_conc).count(0					) != 1:
										raise ValueError("You cannot supply more or less than 2 values"					)
					elif electron_conc < 0:
										raise ValueError("Electron concentration cannot be negative in a semiconductor"					)
					elif hole_conc < 0:
										raise ValueError("Hole concentration cannot be negative in a semiconductor"					)
					elif intrinsic_conc < 0:
										raise ValueError(
										    "Intrinsic concentration cannot be negative in a semiconductor"					)
					elif electron_conc == 0:
										return (
										    "electron_conc",
										    intrinsic_conc**2 / hole_conc,
										)
					elif hole_conc == 0:
										return (
										    "hole_conc",
										    intrinsic_conc**2 / electron_conc,
										)
					elif intrinsic_conc == 0:
										return (
										    "intrinsic_conc",
										    (electron_conc * hole_conc) ** 0.5,
										)
					else:
										return (-1, -1)


if __name__ == "__main__":
					import doctest

					doctest.testmod()




