





import random





def lowerCAmelCase__(__snake_case							)       ->   bool:







	'''simple docstring'''







	lowerCamelCase__              =	num - 1
	lowerCamelCase__              =	0

	while s % 2 == 0:
		lowerCamelCase__              =	s // 2
		t += 1

	for _ in range(5							):
		lowerCamelCase__              =	random.randrange(2 ,num - 1							)
		lowerCamelCase__              =	pow(__snake_case ,__snake_case ,__snake_case							)
		if v != 1:
			lowerCamelCase__              =	0
			while v != (num - 1):
				if i == t - 1:
					return False
				else:
					lowerCamelCase__              =	i + 1
					lowerCamelCase__              =	(v**2) % num
	return True





def lowerCAmelCase__(__snake_case							)       ->   bool:







	'''simple docstring'''







	if num < 2:
		return False

	lowerCamelCase__              =	[
	    2,
	    3,
	    5,
	    7,
	    11,
	    13,
	    17,
	    19,
	    23,
	    29,
	    31,
	    37,
	    41,
	    43,
	    47,
	    53,
	    59,
	    61,
	    67,
	    71,
	    73,
	    79,
	    83,
	    89,
	    97,
	    101,
	    103,
	    107,
	    109,
	    113,
	    127,
	    131,
	    137,
	    139,
	    149,
	    151,
	    157,
	    163,
	    167,
	    173,
	    179,
	    181,
	    191,
	    193,
	    197,
	    199,
	    211,
	    223,
	    227,
	    229,
	    233,
	    239,
	    241,
	    251,
	    257,
	    263,
	    269,
	    271,
	    277,
	    281,
	    283,
	    293,
	    307,
	    311,
	    313,
	    317,
	    331,
	    337,
	    347,
	    349,
	    353,
	    359,
	    367,
	    373,
	    379,
	    383,
	    389,
	    397,
	    401,
	    409,
	    419,
	    421,
	    431,
	    433,
	    439,
	    443,
	    449,
	    457,
	    461,
	    463,
	    467,
	    479,
	    487,
	    491,
	    499,
	    503,
	    509,
	    521,
	    523,
	    541,
	    547,
	    557,
	    563,
	    569,
	    571,
	    577,
	    587,
	    593,
	    599,
	    601,
	    607,
	    613,
	    617,
	    619,
	    631,
	    641,
	    643,
	    647,
	    653,
	    659,
	    661,
	    673,
	    677,
	    683,
	    691,
	    701,
	    709,
	    719,
	    727,
	    733,
	    739,
	    743,
	    751,
	    757,
	    761,
	    769,
	    773,
	    787,
	    797,
	    809,
	    811,
	    821,
	    823,
	    827,
	    829,
	    839,
	    853,
	    857,
	    859,
	    863,
	    877,
	    881,
	    883,
	    887,
	    907,
	    911,
	    919,
	    929,
	    937,
	    941,
	    947,
	    953,
	    967,
	    971,
	    977,
	    983,
	    991,
	    997,
	]

	if num in low_primes:
		return True

	for prime in low_primes:
		if (num % prime) == 0:
			return False

	return rabin_miller(__snake_case							)





def lowerCAmelCase__(__snake_case = 1024							)       ->   int:







	'''simple docstring'''







	while True:
		lowerCamelCase__              =	random.randrange(2 ** (keysize - 1) ,2 ** (keysize)							)
		if is_prime_low_num(__snake_case							):
			return num


if __name__ == "__main__":
			_a						=   generate_large_prime()
			print(("Prime number:", num))
			print(("is_prime_low_num:", is_prime_low_num(num)))










from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_flax_available, is_torch_available


_a						=   {
    "configuration_gpt_neo": ["GPT_NEO_PRETRAINED_CONFIG_ARCHIVE_MAP", "GPTNeoConfig", "GPTNeoOnnxConfig"],
}

try:
			if not is_torch_available():
						raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
			pass
else:
			_a						=   [
			    "GPT_NEO_PRETRAINED_MODEL_ARCHIVE_LIST",
			    "GPTNeoForCausalLM",
			    "GPTNeoForQuestionAnswering",
			    "GPTNeoForSequenceClassification",
			    "GPTNeoForTokenClassification",
			    "GPTNeoModel",
			    "GPTNeoPreTrainedModel",
			    "load_tf_weights_in_gpt_neo",
			]

try:
			if not is_flax_available():
						raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
			pass
else:
			_a						=   [
			    "FlaxGPTNeoForCausalLM",
			    "FlaxGPTNeoModel",
			    "FlaxGPTNeoPreTrainedModel",
			]


if TYPE_CHECKING:
			from .configuration_gpt_neo import GPT_NEO_PRETRAINED_CONFIG_ARCHIVE_MAP, GPTNeoConfig, GPTNeoOnnxConfig

			try:
						if not is_torch_available():
									raise OptionalDependencyNotAvailable()
			except OptionalDependencyNotAvailable:
						pass
			else:
						from .modeling_gpt_neo import (
						    GPT_NEO_PRETRAINED_MODEL_ARCHIVE_LIST,
						    GPTNeoForCausalLM,
						    GPTNeoForQuestionAnswering,
						    GPTNeoForSequenceClassification,
						    GPTNeoForTokenClassification,
						    GPTNeoModel,
						    GPTNeoPreTrainedModel,
						    load_tf_weights_in_gpt_neo,
						)

			try:
						if not is_flax_available():
									raise OptionalDependencyNotAvailable()
			except OptionalDependencyNotAvailable:
						pass
			else:
						from .modeling_flax_gpt_neo import FlaxGPTNeoForCausalLM, FlaxGPTNeoModel, FlaxGPTNeoPreTrainedModel


else:
			import sys

			_a						=   _LazyModule(__name__, globals()["__file__"], _import_structure, module_spec=__spec__)



