Simpler and faster is_prime() recipe.

Author: rhettinger

Doc/library/itertools.rst

@@ -1104,11 +1104,6 @@ The following recipes have a more mathematical flavor:
            data[p*p : n : p+p] = bytes(len(range(p*p, n, p+p)))
        yield from iter_index(data, 1, start=3)
 
-   def is_prime(n):
-       "Return True if n is prime."
-       # is_prime(1_000_000_000_000_403) → True
-       return n > 1 and all(n % p for p in sieve(math.isqrt(n) + 1))
-
    def factor(n):
        "Prime factors of n."
        # factor(99) → 3 3 11
@@ -1123,6 +1118,10 @@ The following recipes have a more mathematical flavor:
        if n > 1:
            yield n
 
+   def is_prime(n):
+       "Return True if n is prime."
+       return n > 1 and next(factor(n)) == n
+
    def totient(n):
        "Count of natural numbers up to n that are coprime to n."
        # https://mathworld.wolfram.com/TotientFunction.html