






import random

from .binary_exp_mod import bin_exp_mod







def       lowercase__	(					A_:						List[str]  ,      A_:						Optional[Any]=1000		)	->				List[str]:







       """simple docstring"""






       if n < 2:
              return False

       if n % 2 == 0:
              return n == 2

       # this means n is odd
       __UpperCAmelCase     				=n - 1
       __UpperCAmelCase     				=0
       while d % 2 == 0:
              d /= 2
              exp += 1

       # n - 1=d*(2**exp)
       __UpperCAmelCase     				=0
       while count < prec:
              __UpperCAmelCase     				=random.randint(2  ,      n - 1		)
              __UpperCAmelCase     				=bin_exp_mod(A_  ,      A_  ,      A_		)
              if b != 1:
                     __UpperCAmelCase     				=True
                     for _ in range(A_		):
                            if b == n - 1:
                                   __UpperCAmelCase     				=False
                                   break
                            __UpperCAmelCase     				=b * b
                            b %= n
                     if flag:
                            return False
                     count += 1
       return True


if __name__ == "__main__":
   __A					=	abs(int(input("Enter bound : ").strip()))
   print("Here's the list of primes:")
   print(", ".join(str(i) for i in range(n + 1) if is_prime_big(i)))







'''simple docstring'''

from collections import defaultdict
from math import gcd

def 					__UpperCamelCase				(						lowercase__    :	int = 1_50_00_00			):






     '''simple docstring'''





     __lowercase      		=defaultdict(lowercase__			)
     __lowercase      		=2
     while 2 * euclid_m * (euclid_m + 1) <= limit:
          for euclid_n in range((euclid_m % 2) + 1,       lowercase__,       2			):
               if gcd(lowercase__,       lowercase__			) > 1:
                    continue
               __lowercase      		=2 * euclid_m * (euclid_m + euclid_n)
               for perimeter in range(lowercase__,       limit + 1,       lowercase__			):
                    frequencies[perimeter] += 1
          euclid_m += 1
     return sum(1 for frequency in frequencies.values() if frequency == 1			)


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


