"""simple docstring"""
import random







def 						__a       (     _SCREAMING_SNAKE_CASE       )     ->bool:
		a__:					Any      							=     num - 1
		a__:					Union[str, Any]      							=     0

		while s % 2 == 0:
				a__:					str      							=     s // 2
				t += 1

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







def 						__a       (     _SCREAMING_SNAKE_CASE       )     ->bool:
		if num < 2:
				return False

		a__:					str      							=     [
		    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(_SCREAMING_SNAKE_CASE       )







def 						__a       (     _SCREAMING_SNAKE_CASE = 1024       )     ->int:
		while True:
				a__:					Tuple      							=     random.randrange(2 ** (keysize - 1)		,					2 ** (keysize)       )
				if is_prime_low_num(_SCREAMING_SNAKE_CASE       ):
						return num


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



"""simple docstring"""
def 						__a       (     _SCREAMING_SNAKE_CASE = 1000000       )     ->int:
  a__:					Any      							=     limit + 1
  a__:					List[str]      							=     [0] * limit
  for first_term in range(1		,					_SCREAMING_SNAKE_CASE       ):
    for n in range(_SCREAMING_SNAKE_CASE		,					_SCREAMING_SNAKE_CASE		,					_SCREAMING_SNAKE_CASE       ):
      a__:					Any      							=     first_term + n / first_term
      if common_difference % 4:  # d must be divisble by 4
        continue
      else:
        common_difference /= 4
        if (
            first_term > common_difference
            and first_term < 4 * common_difference
        ):  # since x,y,z are positive integers
          frequency[n] += 1  # so z>0 and a>d ,also 4d<a

  a__:					Optional[int]      							=     sum(1 for x in frequency[1:limit] if x == 10       )

  return count


if __name__ == "__main__":
 print(f"{solution() = }")


