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From onur, 1 Year ago, written in Python.
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  1. # optimizing fact: It is enough to evaluate the square root of a given number
  2. # in order to determine if that number is prime.
  3. # Reference: David M. Burton - Elementary Number Theory-McGraw-Hill Higher Education (2010)
  4. # page 44, THE SIEVE OF ERATOSTHENES
  5. def prime_numbers(x): # an optimizing fact exists here in terms of time complexity
  6.     square_root = int(x**(1/2))
  7.     count = 0
  8.     for i in range(2, square_root+1):
  9.         if prime_test(i):
  10.             if x % i == 0:
  11.                 count+=1
  12.     if count == 0:
  13.         return True
  14.     else:return False
  15. def prime_test(x): # simply determines if the number is prime
  16.     count = 0
  17.     for i in range(1, x+1):
  18.         if x % i == 0:
  19.             count+=1
  20.     if count == 2:
  21.         return True
  22.     else:return False
  23. #test:
  24. for i in range(500, 600):
  25.     if prime_numbers(i) == True:
  26.         print(i)