



from __future__ import annotations

import math


def A    (							__UpperCamelCase       )    ->   bool:

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


SCREAMING_SNAKE_CASE__   			=   [num for num in range(3, 1_0_0_0_0_1, 2) if not is_prime(num)]


def A    (							__UpperCamelCase       )    ->   list[int]:
			if not isinstance(__UpperCamelCase			,						__UpperCamelCase       ):
						raise ValueError('n must be an integer'       )
			if n <= 0:
						raise ValueError('n must be >= 0'       )

			A__	  =     []
			for num in range(len(__UpperCamelCase       )       ):
						A__	  =     0
						while 2 * i * i <= odd_composites[num]:
									A__	  =     odd_composites[num] - 2 * i * i
									if is_prime(__UpperCamelCase       ):
												break
									i += 1
						else:
									list_nums.append(odd_composites[num]       )
									if len(__UpperCamelCase       ) == n:
												return list_nums

			return []


def A    (							)    ->   int:
			return compute_nums(1       )[0]


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











'''simple docstring'''

import math_equivalence  # From: git+https://github.com/hendrycks/math.git

import datasets


lowercase__		:     str			=							'\\n@article{hendrycksmath2021,\n  title={Measuring Mathematical Problem Solving With the MATH Dataset},\n  author={Dan Hendrycks\n    and Collin Burns\n    and Saurav Kadavath\n    and Akul Arora\n    and Steven Basart\n    and Eric Tang\n    and Dawn Song\n    and Jacob Steinhardt},\n  journal={arXiv preprint arXiv:2103.03874},\n  year={2021}\n}\n'


lowercase__		:     str			=							'\\nThis metric is used to assess performance on the Mathematics Aptitude Test of Heuristics (MATH) dataset.\nIt first canonicalizes the inputs (e.g., converting "1/2" to "\\frac{1}{2}") and then computes accuracy.\n'


lowercase__		:     Dict			=							R'\nCalculates accuracy after canonicalizing inputs.\n\nArgs:\n    predictions: list of predictions to score. Each prediction\n        is a string that contains natural language and LaTex.\n    references: list of reference for each prediction. Each\n        reference is a string that contains natural language\n        and LaTex.\nReturns:\n    accuracy: accuracy after canonicalizing inputs\n        (e.g., converting "1/2" to "\\frac{1}{2}")\n\nExamples:\n    >>> metric = datasets.load_metric("competition_math")\n    >>> results = metric.compute(references=["\\frac{1}{2}"], predictions=["1/2"])\n    >>> print(results)\n    {\'accuracy\': 1.0}\n'
@datasets.utils.file_utils.add_end_docstrings(_DESCRIPTION		,		_KWARGS_DESCRIPTION					)
class 							__lowerCAmelCase	(       datasets.Metric					):






       """simple docstring"""





       def snake_case__		(				self  :						Dict	)       ->	Any:

            '''simple docstring'''




            return datasets.MetricInfo(
                description=_DESCRIPTION			,					citation=_CITATION			,					inputs_description=_KWARGS_DESCRIPTION			,					features=datasets.Features(
                    {
                        '''predictions''': datasets.Value('''string'''	),
                        '''references''': datasets.Value('''string'''	),
                    }	)			,					homepage='''https://github.com/hendrycks/math'''			,					codebase_urls=['''https://github.com/hendrycks/math''']			,					)







       def snake_case__		(				self  :						List[Any]			,					lowerCAmelCase__  :						Dict			,					lowerCAmelCase__  :						int	)       ->	List[str]:

            '''simple docstring'''




            _UpperCamelCase							       =			0.0
            for i, j in zip(lowerCAmelCase__			,					lowerCAmelCase__	):
                 n_correct += 1.0 if math_equivalence.is_equiv(lowerCAmelCase__			,					lowerCAmelCase__	) else 0.0
            _UpperCamelCase							       =			n_correct / len(lowerCAmelCase__	)
            return {
                "accuracy": accuracy,
            }



