
import random


def      UpperCamelCase   (       __lowerCamelCase	:					int       ):
       snake_case			:  Optional[Any]     							= num - 1
       snake_case			:  List[Any]     							= 0

       while s % 2 == 0:
              snake_case			:  Optional[int]     							= s // 2
              t += 1

       for _ in range(5       ):
              snake_case			:  Any     							= random.randrange(2							,   num - 1       )
              snake_case			:  List[Any]     							= pow(__lowerCamelCase							,   __lowerCamelCase							,   __lowerCamelCase       )
              if v != 1:
                     snake_case			:  List[str]     							= 0
                     while v != (num - 1):
                            if i == t - 1:
                                   return False
                            else:
                                   snake_case			:  Dict     							= i + 1
                                   snake_case			:  int     							= (v**2) % num
       return True


def      UpperCamelCase   (       __lowerCamelCase	:					int       ):
       if num < 2:
              return False

       snake_case			:  Dict     							= [
           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(__lowerCamelCase       )


def      UpperCamelCase   (       __lowerCamelCase	:					int = 1024       ):
       while True:
              snake_case			:  List[Any]     							= random.randrange(2 ** (keysize - 1)							,   2 ** (keysize)       )
              if is_prime_low_num(__lowerCamelCase       ):
                     return num


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







import qiskit


def      UpperCamelCase   (       __lowerCamelCase	:					int							,   __lowerCamelCase	:					int       ):
       snake_case			:  int     							= qiskit.Aer.get_backend("aer_simulator"       )

       # Create a Quantum Circuit acting on the q register
       snake_case			:  Dict     							= qiskit.QuantumCircuit(__lowerCamelCase							,   __lowerCamelCase       )

       # Apply X (NOT) Gate to Qubits 0 & 1
       circuit.x(0       )
       circuit.x(1       )

       # Map the quantum measurement to the classical bits
       circuit.measure([0, 1]							,   [0, 1]       )

       # Execute the circuit on the qasm simulator
       snake_case			:  Dict     							= qiskit.execute(__lowerCamelCase							,   __lowerCamelCase							,   shots=1000       )

       # Return the histogram data of the results of the experiment.
       return job.result().get_counts(__lowerCamelCase       )


if __name__ == "__main__":
   __lowerCamelCase				=			single_qubit_measure(2, 2)
   print(F'Total count for various states are: {counts}')





