[3.13] Itertool recipe additions (gh-127483) (gh-127585)

Doc/library/itertools.rst

@@ -877,6 +877,11 @@ and :term:`generators <generator>` which incur interpreter overhead.
        "Returns the sequence elements n times."
        return chain.from_iterable(repeat(tuple(iterable), n))
 
+   def loops(n):
+       "Loop n times. Like range(n) but without creating integers."
+       # for _ in loops(100): ...
+       return repeat(None, n)
+
    def tail(n, iterable):
        "Return an iterator over the last n items."
        # tail(3, 'ABCDEFG') → E F G
@@ -1099,6 +1104,11 @@ 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
@@ -1202,6 +1212,16 @@ The following recipes have a more mathematical flavor:
     [0, 2, 4, 6]
 
 
+    >>> for _ in loops(5):
+    ...     print('hi')
+    ...
+    hi
+    hi
+    hi
+    hi
+    hi
+
+
     >>> list(tail(3, 'ABCDEFG'))
     ['E', 'F', 'G']
     >>> # Verify the input is consumed greedily
@@ -1475,6 +1495,23 @@ The following recipes have a more mathematical flavor:
     True
 
 
+    >>> small_primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97]
+    >>> list(filter(is_prime, range(-100, 100))) == small_primes
+    True
+    >>> carmichael = {561, 1105, 1729, 2465, 2821, 6601, 8911}  # https://oeis.org/A002997
+    >>> any(map(is_prime, carmichael))
+    False
+    >>> # https://www.wolframalpha.com/input?i=is+128884753939+prime
+    >>> is_prime(128_884_753_939)           # large prime
+    True
+    >>> is_prime(999953 * 999983)           # large semiprime
+    False
+    >>> is_prime(1_000_000_000_000_007)     # factor() example
+    False
+    >>> is_prime(1_000_000_000_000_403)     # factor() example
+    True
+
+
     >>> list(factor(99))                    # Code example 1
     [3, 3, 11]
     >>> list(factor(1_000_000_000_000_007)) # Code example 2