improved prime numbers implementation (#1606)

* improved prime numbers implementation

* fixup! Format Python code with psf/black push

* fix type hint

* fixup! Format Python code with psf/black push

* fix doctests

* updating DIRECTORY.md

* added prime tests with negative numbers

* using for instead filter

* updating DIRECTORY.md

* Remove unused typing.List

* Remove tab indentation

* print("Sorted order is:", " ".join(a))

maths/prime_numbers.py

@@ -1,28 +1,34 @@
-from typing import List
+from typing import Generator
 
 
-def primes(max: int) -> List[int]:
+def primes(max: int) -> Generator[int, None, None]:
     """
     Return a list of all primes numbers up to max.
-    >>> primes(10)
-    [2, 3, 5, 7]
-    >>> primes(11)
-    [2, 3, 5, 7, 11]
-    >>> primes(25)
+    >>> list(primes(0))
+    []
+    >>> list(primes(-1))
+    []
+    >>> list(primes(-10))
+    []
+    >>> list(primes(25))
     [2, 3, 5, 7, 11, 13, 17, 19, 23]
-    >>> primes(1_000_000)[-1]
-    999983
+    >>> list(primes(11))
+    [2, 3, 5, 7, 11]
+    >>> list(primes(33))
+    [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31]
+    >>> list(primes(10000))[-1]
+    9973
     """
-    max += 1
-    numbers = [False] * max
-    ret = []
-    for i in range(2, max):
-        if not numbers[i]:
-            for j in range(i, max, i):
-                numbers[j] = True
-            ret.append(i)
-    return ret
+    numbers: Generator = (i for i in range(1, (max + 1)))
+    for i in (n for n in numbers if n > 1):
+        for j in range(2, i):
+            if (i % j) == 0:
+                break
+        else:
+            yield i
 
 
 if __name__ == "__main__":
-    print(primes(int(input("Calculate primes up to:\n>> "))))
+    number = int(input("Calculate primes up to:\n>> ").strip())
+    for ret in primes(number):
+        print(ret)