
from __future__ import annotations

UpperCamelCase_   	=	[True] * 1_0_0_0_0_0_1
UpperCamelCase_   	=	2
while i * i <= 1_0_0_0_0_0_0:
					if seive[i]:
										for j in range(i * i, 1_0_0_0_0_0_1, i):
															UpperCamelCase_   	=	False
					i += 1






def 		_UpperCAmelCase   (	UpperCamelCase:     int  ):






	"""simple docstring"""


	return seive[n]






def 		_UpperCAmelCase   (	UpperCamelCase:     int  ):






	"""simple docstring"""


	return any(digit in "02468" for digit in str(UpperCamelCase  )  )






def 		_UpperCAmelCase   (	UpperCamelCase:     int = 1_0_0_0_0_0_0  ):






	"""simple docstring"""


	__lowerCAmelCase         =							[2]  # result already includes the number 2.
	for num in range(3			,							limit + 1			,							2  ):
		if is_prime(UpperCamelCase  ) and not contains_an_even_digit(UpperCamelCase  ):
			__lowerCAmelCase         =							str(UpperCamelCase  )
			__lowerCAmelCase         =							[int(str_num[j:] + str_num[:j]  ) for j in range(len(UpperCamelCase  )  )]
			if all(is_prime(UpperCamelCase  ) for i in list_nums  ):
				result.append(UpperCamelCase  )
	return result






def 		_UpperCAmelCase   (	):






	"""simple docstring"""


	return len(find_circular_primes()  )


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








import numpy as np
import qiskit






def 		_UpperCAmelCase   (	UpperCamelCase:     int = 8			,							UpperCamelCase:     int | None = None  ):






	"""simple docstring"""


	__lowerCAmelCase         =							np.random.default_rng(seed=UpperCamelCase  )

	# Roughly 25% of the qubits will contribute to the key.
	# So we take more than we need.
	__lowerCAmelCase         =							6 * key_len
	# Measurement basis for Alice's qubits.
	__lowerCAmelCase         =							rng.integers(2			,							size=UpperCamelCase  )
	# The set of states Alice will prepare.
	__lowerCAmelCase         =							rng.integers(2			,							size=UpperCamelCase  )
	# Measurement basis for Bob's qubits.
	__lowerCAmelCase         =							rng.integers(2			,							size=UpperCamelCase  )

	# Quantum Circuit to simulate BB84
	__lowerCAmelCase         =							qiskit.QuantumCircuit(UpperCamelCase			,							name="BB84"  )

	# Alice prepares her qubits according to rules above.
	for index, _ in enumerate(UpperCamelCase  ):
		if alice_state[index] == 1:
			bbaa_circ.x(UpperCamelCase  )
		if alice_basis[index] == 1:
			bbaa_circ.h(UpperCamelCase  )
	bbaa_circ.barrier()

	# Bob measures the received qubits according to rules above.
	for index, _ in enumerate(UpperCamelCase  ):
		if bob_basis[index] == 1:
			bbaa_circ.h(UpperCamelCase  )

	bbaa_circ.barrier()
	bbaa_circ.measure_all()

	# Simulate the quantum circuit.
	__lowerCAmelCase         =							qiskit.Aer.get_backend("aer_simulator"  )
	# We only need to run one shot because the key is unique.
	# Multiple shots will produce the same key.
	__lowerCAmelCase         =							qiskit.execute(UpperCamelCase			,							UpperCamelCase			,							shots=1			,							seed_simulator=UpperCamelCase  )
	# Returns the result of measurement.
	__lowerCAmelCase         =							job.result().get_counts(UpperCamelCase  ).most_frequent()

	# Extracting the generated key from the simulation results.
	# Only keep measurement results where Alice and Bob chose the same basis.
	__lowerCAmelCase         =							"".join(
	    [
	        result_bit
	        for alice_basis_bit, bob_basis_bit, result_bit in zip(
	            UpperCamelCase			,							UpperCamelCase			,							UpperCamelCase  )
	        if alice_basis_bit == bob_basis_bit
	    ]  )

	# Get final key. Pad with 0 if too short, otherwise truncate.
	__lowerCAmelCase         =							gen_key[:key_len] if len(UpperCamelCase  ) >= key_len else gen_key.ljust(UpperCamelCase			,							"0"  )
	return key


if __name__ == "__main__":
					print(f'''The generated key is : {bbaa(8, seed=0)}''')
					from doctest import testmod

					testmod()






