





import math
import unittest



def    __lowercase   (      _SCREAMING_SNAKE_CASE	) ->   bool:


      '''simple docstring'''


      assert isinstance(_SCREAMING_SNAKE_CASE ,						_SCREAMING_SNAKE_CASE	) and (
          number >= 0
      ), "'number' must been an int and positive"

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

class 		UpperCamelCase__ (      unittest.TestCase   ):



     '''simple docstring'''

     def 				SCREAMING_SNAKE_CASE__  (							self						:    Dict       )     ->		Tuple:




           '''simple docstring'''


           self.assertTrue(is_prime(2       )       )
           self.assertTrue(is_prime(3       )       )
           self.assertTrue(is_prime(5       )       )
           self.assertTrue(is_prime(7       )       )
           self.assertTrue(is_prime(11       )       )
           self.assertTrue(is_prime(13       )       )
           self.assertTrue(is_prime(17       )       )
           self.assertTrue(is_prime(19       )       )
           self.assertTrue(is_prime(23       )       )
           self.assertTrue(is_prime(29       )       )






     def 				SCREAMING_SNAKE_CASE__  (							self						:    Optional[int]       )     ->		Tuple:




           '''simple docstring'''


           with self.assertRaises(lowerCamelCase__       ):
                 is_prime(-19       )
           self.assertFalse(
               is_prime(0       )						,"""Zero doesn't have any positive factors, primes must have exactly two."""						,)
           self.assertFalse(
               is_prime(1       )						,"""One only has 1 positive factor, primes must have exactly two."""						,)
           self.assertFalse(is_prime(2 * 2       )       )
           self.assertFalse(is_prime(2 * 3       )       )
           self.assertFalse(is_prime(3 * 3       )       )
           self.assertFalse(is_prime(3 * 5       )       )
           self.assertFalse(is_prime(3 * 5 * 7       )       )


if __name__ == "__main__":
      unittest.main()









from collections import defaultdict
from math import gcd



def    __lowercase   (      _SCREAMING_SNAKE_CASE = 1_50_00_00	) ->   int:


      '''simple docstring'''


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


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


