import math





def     UpperCAmelCase						(   lowercase							):







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





def     UpperCAmelCase						(   lowercase = 1000							,      lowercase = 1000							):







				"""simple docstring"""



				__lowercase			      =							[0, 0, 0]  # length, a, b
				for a in range((a_limit * -1) + 1							,      lowercase							):
								for b in range(2							,      lowercase							):
												if is_prime(lowercase							):
																__lowercase			      =							0
																__lowercase			      =							0
																while is_prime((n**2) + (a * n) + b							):
																				count += 1
																				n += 1
																if count > longest[0]:
																				__lowercase			      =							[count, a, b]
				__lowercase			      =							longest[1] * longest[2]
				return ans


if __name__ == "__main__":
		print(solution(1_0_0_0, 1_0_0_0))
import json
import os
import tempfile

import datasets
from utils import generate_example_dataset, get_duration


__a  :					int          =  5_0_0_0_0_0

__a   ,						__a  :					Any          =  os.path.split(__file__)
__a  :					Dict          =  os.path.join(RESULTS_BASEPATH, """results""", RESULTS_FILENAME.replace(""".py""", """.json"""))





@get_duration
def     UpperCAmelCase						(   lowercase							):







				"""simple docstring"""



				__lowercase			      =							dataset.select(range(0							,      len(lowercase							)							,      2							)							)





@get_duration
def     UpperCAmelCase						(   lowercase							):







				"""simple docstring"""



				__lowercase			      =							dataset.sort('''numbers'''							)





@get_duration
def     UpperCAmelCase						(   lowercase							):







				"""simple docstring"""



				__lowercase			      =							dataset.shuffle()





@get_duration
def     UpperCAmelCase						(   lowercase							):







				"""simple docstring"""



				__lowercase			      =							dataset.train_test_split(0.1							)





@get_duration
def     UpperCAmelCase						(   lowercase							,      lowercase=10							):







				"""simple docstring"""



				for shard_id in range(lowercase							):
								__lowercase			      =							dataset.shard(lowercase							,      lowercase							)





def     UpperCAmelCase						(   ):







				"""simple docstring"""



				__lowercase			      =							{'''num examples''': SPEED_TEST_N_EXAMPLES}
				__lowercase			      =							(select, sort, shuffle, train_test_split, shard)
				with tempfile.TemporaryDirectory() as tmp_dir:
								print('''generating dataset'''							)
								__lowercase			      =							datasets.Features({'''text''': datasets.Value('''string'''							), '''numbers''': datasets.Value('''float32'''							)}							)
								__lowercase			      =							generate_example_dataset(
								    os.path.join(lowercase							,      '''dataset.arrow'''							)							,      lowercase							,      num_examples=lowercase							)
								print('''Functions'''							)
								for func in functions:
												print(func.__name__							)
												__lowercase			      =							func(lowercase							)

				with open(lowercase							,      '''wb'''							) as f:
								f.write(json.dumps(lowercase							).encode('''utf-8'''							)							)


if __name__ == "__main__":  # useful to run the profiler
		benchmark_indices_mapping()