




'''simple docstring'''





import math


def   UpperCamelCase_(			snake_case							: int  ):

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


def   UpperCamelCase_(			snake_case							: int = 1_0_0_0							,       snake_case							: int = 1_0_0_0  ):

							'''simple docstring'''






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


if __name__ == "__main__":
		print(solution(1000, 1000))










'''simple docstring'''





import qiskit
from qiskit.providers import Backend


def   UpperCamelCase_(			snake_case							: int							,       snake_case							: int  ):

							'''simple docstring'''






							snake_case_      ,   snake_case_			      =   bin(snake_case  )[2:], bin(snake_case  )[2:]  # Remove leading '0b'

							# Ensure that both strings are of the same length
							if len(snake_case  ) > len(snake_case  ):
														snake_case_			      =   y.zfill(len(snake_case  )  )
							else:
														snake_case_			      =   x.zfill(len(snake_case  )  )

							# We need (3 * number of bits in the larger number)+1 qBits
							# The second parameter is the number of classical registers, to measure the result
							snake_case_			      =   qiskit.QuantumCircuit((len(snake_case  ) * 3) + 1							,       len(snake_case  ) + 1  )

							# We are essentially "not-ing" the bits that are 1
							# Reversed because it's easier to perform ops on more significant bits
							for i in range(len(snake_case  )  ):
														if x[::-1][i] == "1":
																					circuit.x(snake_case  )
							for j in range(len(snake_case  )  ):
														if y[::-1][j] == "1":
																					circuit.x(len(snake_case  ) + j  )

							return circuit, x, y


def   UpperCamelCase_(			snake_case							: qiskit.QuantumCircuit							,       snake_case							: int							,       snake_case							: int							,       snake_case							: int							,       snake_case							: int							,       ):

							'''simple docstring'''






							circuit.ccx(snake_case							,       snake_case							,       snake_case  )
							circuit.cx(snake_case							,       snake_case  )
							circuit.ccx(snake_case							,       snake_case							,       snake_case  )
							circuit.cx(snake_case							,       snake_case  )
							circuit.cx(snake_case							,       snake_case  )


def   UpperCamelCase_(			snake_case							: int							,       snake_case							: int							,       snake_case							: Backend = qiskit.Aer.get_backend("aer_simulator"  )							,       ):

							'''simple docstring'''






							if vala < 0 or vala < 0:
														raise ValueError("Both Integers must be positive!"  )

							# Store the Integers
							snake_case_      ,   snake_case_      ,   snake_case_			      =   store_two_classics(snake_case							,       snake_case  )
							for i in range(len(snake_case  )  ):
														full_adder(snake_case							,       snake_case							,       len(snake_case  ) + i							,       len(snake_case  ) + len(snake_case  ) + i							,       len(snake_case  ) + len(snake_case  ) + i + 1  )
														circuit.barrier()  # Optional, just for aesthetics

							# Measure the resultant qBits
							for i in range(len(snake_case  ) + 1  ):
														circuit.measure([(len(snake_case  ) * 2) + i]							,       [i]  )

							snake_case_			      =   qiskit.execute(snake_case							,       snake_case							,       shots=1  ).result()

							# The result is in binary. Convert it back to int
							return int(list(res.get_counts()  )[0]							,       2  )


if __name__ == "__main__":
		import doctest

		doctest.testmod()




