improved prime number generator to check only up to sqrt(n) instead of n

maths/prime_numbers.py

@@ -1,7 +1,8 @@
 from typing import Generator
+import math
 
 
-def primes(max: int) -> Generator[int, None, None]:
+def slow_primes(max: int) -> Generator[int, None, None]:
     """
     Return a list of all primes numbers up to max.
     >>> list(primes(0))
@@ -28,6 +29,35 @@ def primes(max: int) -> Generator[int, None, None]:
             yield i
 
 
+def primes(max: int) -> Generator[int, None, None]:
+    """
+    Return a list of all primes numbers up to max.
+    >>> list(primes(0))
+    []
+    >>> list(primes(-1))
+    []
+    >>> list(primes(-10))
+    []
+    >>> list(primes(25))
+    [2, 3, 5, 7, 11, 13, 17, 19, 23]
+    >>> 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
+    """
+    numbers: Generator = (i for i in range(1, (max + 1)))
+    for i in (n for n in numbers if n > 1):
+        # only need to check for factors up to sqrt(i)
+        bound = int(math.sqrt(i)) + 1
+        for j in range(2, bound):
+            if (i % j) == 0:
+                break
+        else:
+            yield i
+
+
 if __name__ == "__main__":
     number = int(input("Calculate primes up to:\n>> ").strip())
     for ret in primes(number):