


"""simple docstring"""
from maths.prime_check import is_prime







def   _a			( _SCREAMING_SNAKE_CASE			)      ->			int:
							if not isinstance(_SCREAMING_SNAKE_CASE			,	_SCREAMING_SNAKE_CASE			):
														snake_case_          =						f"""Input value of [number={number}] must be an integer"""
														raise TypeError(_SCREAMING_SNAKE_CASE			)
							if is_prime(_SCREAMING_SNAKE_CASE			) and is_prime(number + 2			):
														return number + 2
							else:
														return -1


if __name__ == "__main__":
				import doctest

				doctest.testmod()







"""simple docstring"""
from collections import defaultdict
from math import gcd







def   _a			( _SCREAMING_SNAKE_CASE = 1_500_000			)      ->			int:
							snake_case_          =						defaultdict(_SCREAMING_SNAKE_CASE			)
							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
																					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() = }""")



