# optimizing fact: It is enough to evaluate the square root of a given number
# in order to determine if that number is prime.
# Reference: David M. Burton - Elementary Number Theory-McGraw-Hill Higher Education (2010)
# page 44, THE SIEVE OF ERATOSTHENES
def prime_numbers(x): # an optimizing fact exists here in terms of time complexity
    square_root = int(x**(1/2))
    count = 0
    for i in range(2, square_root+1):
        if prime_test(i):
            if x % i == 0:
                count+=1
    if count == 0:
        return True
    else:return False
def prime_test(x): # simply determines if the number is prime
    count = 0
    for i in range(1, x+1):
        if x % i == 0:
            count+=1
    if count == 2:
        return True
    else:return False
#test:
for i in range(500, 600):
    if prime_numbers(i) == True:
        print(i)